⼤學數學

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2014 組合數學新苗研討會

⼤學數學

2014 8 2 3

⼤會演講

李國偉教授中央研究院

林強教授中央大學數學系

台灣師範大學公館校區科教大樓 5 樓演講廳

科技部自然司數學研究推動中心

國家理論科學研究中心數學組 (臺北辦公室) 東賢實業股份有限公司

游森棚 (台灣師範大學數學系)

林延輯 (台灣師範大學數學系)

郭君逸 (台灣師範大學數學系)

徐泰煒 (台灣師範大學僑先部)

張飛黃 (台灣師範大學僑先部)

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⼤會宗旨

組合數學新苗研討會最初由中央研究院數學研究所李國偉教授在 1990 年發起，

每年由各大學或相關研究機構輪流主辦，此研討會所舉辦的目的在於提供台灣組合數學相關領域的應屆碩博畢業生與相關研究人員，發表其研究成果，互相交流或討論，以獲得後續研究方向的機會。除此之外，也提供與會者互相聯絡、切磋及觀摩的平台。

適逢今年是第 25 週年舉辦，我們邀請李國偉教授，與林強教授，擔任大會演講，兩位資深教授在組合領域上有相當豐碩的研究成果，同時，他們也都是第一屆新苗研討會的發起者，相信其研究經驗能夠給予後輩良好的啟發與鼓勵。此研討會對於鼓勵青年新進之輩與國內學者專家之研究交流有很大的助益，故組合數學新苗研討會，一直是台灣組合數學界中相當重要的研討會之一。此外，於今年還特地邀請大陸與日本組合領域的博士生一起來參與盛會，相信藉由這樣的交流，

能為組合新苗研討會帶來新的風貌。

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新苗

新苗研討會是台灣組合數學界的年度盛事。只要在國內的組合數學圈子，提起

新苗一定有很多故事可以說 — 我還記得某一次茶敘時大家笑著說：「“離散”與

“組合”這兩個字面意義相反的詞居然是同一件事!」

開辦新苗研討會是令人佩服的遠見。多年來，新苗見證了數以百計的新科碩士與博士的畢業，培養了許多人才，見證了台灣組合數學從無到有的興盛。組合數學這個相對年輕的領域能夠在台灣形成一個不可忽視的研究聚落，新苗研討會開疆闢土的開拓功不可沒。

而新苗今年滿二十五歲了 — 和應屆的碩士畢業生一樣大！一個研討會可以二十五週年真是不簡單的。籌備委員會花了許多的時間，上下蒐羅迄今的所有新苗書面議程，放在今年的網頁上。非常幸運的是，我們找到了第一屆的議程。1990 年的第一屆新苗在中央研究院舉行，六個 sessions 的主持人中，包括了發起人李國偉教授與今年即將榮退的林強教授。多年來兩位教授在台灣組合界培育了許多學者持續活躍於學界，對台灣組合界有很大的貢獻。我們非常榮幸邀請兩位教授擔任今年的大會演講。

承襲往年作法，今年我們亦有最佳論文的評選。但無論有沒有得獎，都祝福所有從新苗畢業的新科碩士與博士。各位是台灣組合數學界的新苗，有朝一日將成為參天大樹。恭喜畢業!

謹代表籌備委員會歡迎大家蒞臨今年的新苗研討會。這是台師大首度承辦，雖只有短短的兩天，我們仍希望能盡力做到最好。張飛黃與郭君逸兩位教授扛下了大部分的籌備工作，林延輯與徐泰煒 (第一屆新苗的演講者，亦為林強教授的第一位學生) 兩位教授亦協助甚多。倘有不盡完美之處，就請多多包涵。

二十五年是一個里程碑。承先啟後，讓我們一起努力，往下一個二十五年邁進。

國立台灣師範大學數學系

“教官”/游森棚 2014/8/2

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2014 組合數學新苗研討會議程

8 2 ( )

08:45–09:30 ( ⼤ )

09:30–09:45

09:50–10:35 ⼤會演講 ( 數學)

Graph labellings: splittable graph and antimagic graphs

10:35–11:00 ( 數學)

11:00–11:20

Session 1 501 503

11:20–11:40 ( 數學) ( 數學)

11:40–12:00 ( ⼤數) ( ⼤數)

12:00–14:00 14:00–14:25

邀請演講 ( ⼤ )

The spectral redius of connected graphs with the independence number

14:25–14:50 邀請演講 ( ⼤ )

On aﬃne-invariant strictly cyclic Steiner quadruple systems 14:50–15:10

Session 2 501 503

15:10–15:30 ( ⼤數) ( ⼤數)

15:30–15:50 ( ⼤ ) ( 數)

15:50–16:10 博 ( ⼤數) ( 數學)

Session 3 501 503

16:20–16:40 ( ⼤數) ( ⼤數學)

16:40–17:00 ( ⼤數) ( ⼤數)

17:00–17:20 ( ⼤數)

17:20– ⼤合 &

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8 3 ( )

08:30–09:15 ⼤會演講 ( 研數學 )

Rota’s Lessons 09:15–09:40

邀請演講 ( 數學)

Lovász Local Lemma, Entropy Compression and Graph Colorings

09:40–10:00 Session 4

10:00–10:25 ( 研數學 )

10:25–10:50 ( ⼤數)

10:50–11:15 ( ⼤數)

Session 5

11:25–11:50 ( 數學)

11:50–12:15 ( 數學)

12:15–14:00 14:00–14:25

邀請演講 ( ⼤ )

Which connected graphs are determined by their distance spectra

14:25–14:50 ( ⼤數)

Session 6

15:00–15:25 ( ⼤數)

15:25–15:50 ( ⼤數學)

16:00–16:30

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⼤會演講

Graph Labellings: Splittable Graphs and Antimagic Graphs

Chiang Lin ( )

Department of Mathematics, National Central University ( ⼤學數學 ) 1. Splittable Graph.

Let G be a graph. Then G is t-splittable if the edges of G can be partitioned into t isomorphic graphs. A trivial necessary condition for G to be t-splittable is that|E(G)| = 0 (mod t).

(1) We give the necessary and suﬃcient conditions for the spiders to be t- splittable.

(2) We investigate the 2-splittabilities of multipaths and multicycles with mul- ticity 2, respectively.

2. Antimagic Graphs.

Let G be a graph. If f : E(G) → A where A ⊂ C, then for v ∈ V (G), the vertex sum of f at v is f⁺(v) = ∑

uv∈E(G)f (uv). If there exists f : E(G) → {1, 2, . . . , |E(G)|}, 1-1 such that all vertex sums of f are distinct, then G is an- timagic. A well-known conjecture is that every simple connected graph except K₂ is antimagic. We investigate the antimagicnesses of disconnected graphs and multigraphs.

(a) We investigate the antimagicness of star forests.

(b) The union of a path (of order ≥ 3) and a star (of order ≥ 3) is antimagic.

(c) Any multipath with multiplicity 2 and maximum degree≤ 3 is antimagic.

3. A Generalization of Antimagic Graphs.

Let G be a graph. If A⊂ C with |A| = |E(G)| and there exists f : E(G) → A, 1-1 such that all f⁺(x) (x ∈ V (G)) are distinct, then G is A-antimagic. If B ⊂ C with |B| ≥ |E(G)|, and G is A-antimagic for every A with A ⊂ B and

|A| = |E(G)|, then G is B-antimagic. Trivially, for a graph G, if B1 ⊂ B2 ⊂ C,

|B1| ≥ |E(G)|, and G is B2-antimagic, then G is B₁-antimagic.

(a) Let G be a graph. Then G isR-antimagic if and only if G is C-antimagic.

(b) Any path of order ≥ 5 is R-antimagic.

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Rota’s Lessons

Ko-Wei Lih ( )

Institute of Mathematics, Academia Sinica ( 研數學 )

Gian-Carlo Rota(1932 – 1999) 20 組合數學數學

學數學學合 Rota 學博

Fabrizio Palombi “Indiscrete Thoughts”

演講 18 “Ten Lessons I Wish I Had Been Taught” 19 “Ten Lessons for the Survival of a Mathematics Department”

Rota

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邀請演講

Lovász Local Lemma, Entropy Compression and Graph Colorings

Hsin-Hao Lai ( )

Department of Mathematics, National Kaohsiung Normal University

( ⼤學數學 )

In the 70’s, Lovász introduced the Lovász local lemma. Lovász local lemma is a powerful probabilistic method and has been used widely in the study of graph colorings.

In [1], an inspiring method, called the entropy compression, was introduced. It is an algorithmic version of Lovász local lemma and has been used in the study of graph colorings.

In this talk, I will introduce the relation between Lovász local lemma and entropy compression. Also, I will introduce the results of graph colorings obtained by entropy compression and describe the idea behind the method.

Keywords: Lovász Local Lemma, Entropy Compression, Graph Coloring.

Reference

[1] R. Moser, G. Tardos, A constructive proof of the general Lovász local lemma, J.

ACM 57 (2010), Art. 11.

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Which connected graphs are determined by their distance spectra

Huiqiu Lin ( )

Department of Mathematics, East China University of

Science and Technology ( ⼤ )

The distance matrix D(G) = (d_ij)_n_×n of a connected graph G is the matrix indexed by the vertices of G, where d_ij denotes the distance between the vertices v_i and v_j. Two nonisomorphic graphs with the same D-spectra are called cospectral.

We say that a graph is determined by the D-spectra if there is no other nonisomorphic graph with the same D-spectra. In this talk, we characterize some graphs which are determined by their D-spectra.

The spectral radius of connected graphs with the independence number ^*

Ya-Lei Jin ( )

Department of Mathematics, and MOE-LSC, Shanghai Jiao Tong University ( ⼤ )

In this talk, we investigate some properties of the Perron vector of connected graphs. These results are used to characterize all extremal connected graphs which attain the minimum value among the spectral radii of all connected graphs with order n = kα and the independence number α. Moreover, all extremal graphs which attain the maximum value among the spectral radii of clique trees with order n = kα and the independence number α are characterized.

*This work is joint with my advisor Xiao-Dong Zhang( ).

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On aﬃne-invariant strictly cyclic Steiner quadruple systems

Xiao-Nan Lu ( )

Graduate School of Information Science, Nagoya University, Nagoya, Japan (

⼤⼤研 )

Advisor: Professor Masakazu Jimbo

A Steiner quadruple system of order v, denoted by SQS(v), is a pair (V,B), where V is a ﬁnite set of v elements, andB is a collection of 4-elements subsets of V , called blocks or quadruples, such that each 3-elements subset (triple) of V is contained in exactly one block inB.

Let G be a permutation group on V . If G leaves B invariant, then G is called an automorphism group of SQS(v). In particular, an SQS(v) is said to be cyclic if it admits a cyclic group of order v. Accordingli,B can be partitioned into orbits under the cyclic permutations. Furthermore, the orbit whose cardinality is equal to v is said to be full. If all the orbits are full, then the SQS(v) is said to be strictly cyclic, denoted by sSQS(v).

Without loss of generality, for a cyclic SQS (V,B), we can identify V with Zv, the additive group of integers modulo v. Moreover, we consider the multiplicative group of all units of Zv, say Z^×v. If an SQS admits all the elements in Z^×v as multipliers, then it is said to be aﬃne-invariant.

It is easy to show that an sSQS(v) exists only if v ≡ 2, 10 (mod 24). The con- structions of sSQS’s was ﬁrst studied by Köhler in 1979. Köhler proposed a graph named after him, and proved that an sSQS(v) exists if and only if the corresponding Köhler’s graph has a 1-factors. But there are few constructions known for sSQS(v) which are independent from Köhler’s.

In this talk, we suppose v = 2p, where p ≡ 1, 5 (mod 12) is an odd prime, and focus on the constructions of aﬃne-invariant sSQS(v). By means of a system of generators of projective special linear group PSL(2, p), we deﬁne two families of graphs algebraically whose 1-factors play an important role in our constructions. By computer search, we also verify that all these graphs for p < 100, 000 have 1-factors.

Futhermore, we give recursive constructions for aﬃne-invariant sSQS(2p^m), for any positive integer m.

Keywords: Steiner quadruple system, projective linear group, 1-factor.

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博⼠

Maximum packings and minimum coverings of multigraphs with paths and stars

Chun-Cheng Chen ( )

Department of Mathematics, National Central University ( ⼤學數學 ) Joint work with Hung-Chih Lee( )

Let F , G, and H be multigraphs. An (F, G)-decomposition of H is an edge decomposition of H into copies of F and G using at least one of each. For subgraphs L and R of H, an (F, G)-packing (resp. (F, G)-covering) of H with leave L (resp.

padding R) is an (F, G)-decomposition of H − E(L) (resp. H+E(R)). An (F, G)- packing (resp. (F, G)-covering) of H with the largest (resp. smallest) cardinality is a maximum (F, G)-packing (resp. minimum (F, G)-covering), and its cardinality is referred to as the (F, G)-packing number (resp. (F, G)-covering number) of H.

Let k be a positive integer. A k-path, denoted by P_k, is a path on k vertices. A k-star, denoted by S_k, is a star with k edges. In this paper, we determine the packing numbers and the covering numbers of both λKn and λKn,n with (k + 1)-paths and k-stars for any λ, n and k. Moreover, necessary and suﬃcient conditions for the existence of (P_k+1, S_k)-decompositions of both λK_n and λK_n,n are given.

Keywords: Packing, Covering, Path, Star.

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Factorizations of Suﬃxes of Two-Way Inﬁnite Characteristic Words

Fang-Yi Liao ( )

Department of Applied Mathematics,

Chung Yuan Christian University ( ⼤學數 ) Advisor: Wai-Fong Chuan( )

Let α be an irrational number between 0 and 1 with continued fraction expansion [0; a₁ + 1, a₂, a₃,· · · ], where an ≥ 1 (n ≥ 1). Deﬁne a sequence of numbers {qn}n≥1

by q₋₁ = 1, q₀ = 1, q_n = a_nq_n₋₁ + q_n₋₂ (n ≥ 1). For each integer k ≥ −1, we con- sider the kth-order factorization of each suffix H of a two-way infinite characteristic word of α of the form: H = u_ku_k+1u_k+2· · · , where the length of the factor ui is q_i (i ≥ k). We show that in such a factorization, either all ui are singular words, or there exists a nonnegative integer q such that H begins with q singular words, and u_k+q, u_k+q+1, u_k+q+2,· · · are α-words. Moreover, the labels of these α-words are uniquely determined by the F -representation of a nonnegative integer obtained from the position of H in the two-way infinite characteristic word.

Next, define Markov word pattern of order k (k ≥ −1) generated by a pair of seed words (u, v) as follows: M_k(u, v) = z₁z₂z₃· · · , where z1 = u, z₂ = v, and z_i = z_iâ₋₁î+k⁻¹⁻¹z_i₋₂z_i₋₁ (i ≥ 3). We show that each suffix H of each two-way infinite characteristic word is a Markov word pattern, and the pairs of its seed words obtained are adjacent α-words; we also find all possible pairs of seed words of H which are pairs of adjacent α-words. On the other hand, we show that each Markov word pattern generated by any pair of adjacent α-words is a suffix of a two-way infinite characteristic word.

Finally, we study the set V of all pairs of adjacent α-words. We describe the elements of V in terms of cyclic shifts, lexicographic order, and labels. For each α-word w, we find all possible words u such that (u, w) (resp., (w, u)) are pairs of adjacent α-words. Also, we construct a directed graph G_α consisting of the vertex set of all α-words and the edge set V , and use such a graph to illustrate the results about adjacent α-words, and the suffixes of the two-way infinite characteristic words that they generate.

Keywords: Two-way inﬁnite characteristic word, Factorization, Markov word pattern, Seed word, Adjacent α-word.

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Self-stabilizing Minimal Dominating Set Algorithms of Distributed Systems and the Signed Star Domination Number

of Cayley Graphs

Well Y. Chiu ( )

National Chiao Tung University ( ⼤學數 ) Advisor: Chiuyuan Chen( )

The study of the domination problem in graph theory began in the nineteen- sixties. A distributed system such as an ad hoc network can be modeled by an undirected simple graph G = (V, E), where V represents the set of nodes (i.e., processes) and E represents the set of interconnections between processes of the distributed system. A subset D of the vertex set V of G is a dominating set if each vertex v∈ V is either a member of D or adjacent to a vertex in D. A dominating set of G is a minimal dominating set (MDS) if none of its proper subsets is a dominating set of G. An MDS has an application of clustering in wireless networks and is maintained for minimizing the number of required resource centers.

Self-stabilization is a concept of designing a distributed system for transient fault toleration and was introduced by Dijkstra in 1974. A distributed system is self- stabilizing if, regardless of its initial configuration, the system is guaranteed to reach a legitimate (i.e., correct) configuration in a finite time. Here the system configuration consists of the state of every process. A self-stabilizing algorithm comprises a collection of rules and each rule has a trigger precondition and an action. The action changes the state of the node by updating its variables. An execution of a rule is called a move. The performance of the proposed algorithms of this thesis is measured by the total number of moves executed by an algorithm. Various execution models have been used in self-stabilizing algorithms and these are encapsulated with the notion of daemons. A daemon can be fair or unfair. It is well-known that an unfair distributed daemon is more practical than other types of daemons.

Let n denote the number of nodes (processes) in a given distributed system. In 2007, Turau proposed the ﬁrst linear-time self-stabilizing algorithm for the MDS problem under an unfair distributed daemon; this algorithm stabilizes in at most 9n moves. In 2008, Goddard et al. improved the result to a 5n-move algorithm.

It is interesting to develop an algorithm that takes less moves than the best known result—5n moves using an unfair distributed daemon. In this thesis, we will present a 4n-move self-stabilizing MDS algorithm using an unfair distributed daemon.

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It is desired that an MDS algorithm is MDS-silent, which means that if the orig- inal conﬁguration of the distributed system is already an MDS, then the algorithm should not make any move. Note that in the normal model, a node can only access the information of its 1-hop neighbors and we call such information distance-1 information. Unfortunately, in this thesis we will prove that distance-1 information is not suﬃcient for building up an MDS-silent algorithm for a distributed system.

What will happen if a node can access the information of its k-hop neighbors for k ≥ 2? In this thesis, we will discuss this problem and propose a new performance measure, called stableness, for self-stabilizing MDS algorithms. We also generalize this result to categorize all self-stabilizing algorithms into four levels. In particular, we will show that a self-stabilizing MDS-silent algorithm can be built up under the distance-2 model and the stabilizing time is upper bounded by 2n.

Let G be a simple connected graph with vertex set V (G) and edge set E(G). A function f : E(G) → {−1, 1} is called a signed star dominating function (SSDF) on G if ∑

e∈EG(v)f (e) ≥ 1 for every v ∈ V (G), where EG(v) is the set of all edges incident to v. The signed star domination number of G is deﬁned as γSS(G) = min{∑

e∈E(G)f (e)| f is an SSDF on G}. Let D be a ﬁnite digraph with vertex set V (D) and arc set A(D). For each vertex v ∈ V (D), let A(v) be the set of all out-going arcs from v. By replacing E(v) by A(v), one can deﬁne SSDF on D and γ_SS(D) = min{∑

a∈A(D)f (a) | f is an SSDF on D}. Let Γ be a ﬁnite nontrivial group and S be a nonempty subset of Γ. The Cayley digraph Cay_D(Γ, S) is the digraph whose vertices are the elements of Γ, and there is an arc from α to ασ whenever α∈ Γ and σ ∈ S. Let Ω be a symmetric generating subset of nonidentity elements of Γ. The Cayley graph Cay(Γ, Ω) corresponding to Γ and Ω is the ordinary graph with vertex set Γ and edge set E ={{α, ασ} | α ∈ Γ, σ ∈ Ω}. In this thesis, we obtain exact values for the signed star domination number of all Cayley digraphs Cay_D(Γ, S) and certain classes of Cayley graphs Cay(Γ, Ω), which is later generalized to{2, 1}-factorable graphs.

Keywords: self-stabilizing, minimal dominating set, stableness, signed star dom- ination number.

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Decycling Number on Graphs and Digraphs

Min-Yun Lien ( )

National Chiao Tung University ( ⼤學數 ) Advisor: Hung-Lin Fu( )

A set of vertices of a graph or an digraph whose removal induces an acyclic graph is referred as a decycling set, or a feedback vertex set, of the graph. The minimum cardinality of a decycling set of a graph G is referred to as the decycling number of G.

The problem of determining the decycling number has been proved to be NP- complete for general graphs, which also shows that even for planar graphs, bipartite graphs and perfect graphs, the computation complexity of ﬁnding their decycling numbers is not reduced.

The problem of destroying all cycles in a graph by deleting a set of vertices originated from applications in combinatorial circuit design. Also, it has found applications in deadlock prevention in operating systems, the constraint satisfaction problem and Bayesian inference in artiﬁcial intelligence, monopolies in synchronous distributed systems, the converters’ placement problem in optical networks, and VLSI chip design.

In this talk, we introduce the decycling number of graphs and also digraphs.

The graphs we consider are outerplanar graphs and grid graphs P_mPn. For the first class of graphs, we characterize their decycling number by way of the cycle packing number and for grid graphs, we improve the known results to obtain either tight bounds or exact values. On digraphs, we consider generalized Kautz digraphs and generalized de Bruijn digraphs. Mainly, we use a novel idea in which we find a sequence of subsets of vertex set satisfying certain conditions and then obtain a decycling set. This provides an upper bound of the decycling number of digraphs we consider. Note that this idea can be applied to find the decycling set of general digraphs.

Keywords: Decycling Number, Feedback vertex number, Outerplanar Graphs, PmPn, Generalized Kautz Digraphs, Generalized de Bruijn Digraphs.

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Optimally ℓ-Pebbling Cycles

H. X. Chiang ( )

Department of Mathematics,

Chung Yuan Christian University ( ⼤學數 ) Joint work with Chin-Lin Shiue and M. M. Wong

Let G be a graph. A distribution of pebbles of G is a a function δ : V (G) → N ∪ {0}. In a graph with a distribution of pebbles, a pebbling move consists of removing two pebbles from one vertex and then placing one pebble at an adjacent vertex. A pebbling type α of G is a mapping from V (G) intoN∪

{0}. A distribution δ is called an α-pebbling if whenever we choose a target vertex v, we can move α(v) pebbles to v by applying pebbling moves repeatedly ( if necessary). An it ℓ- pebbling of G is an α-pebbling of G for which α(v) = ℓ for each v ∈ V (G), where ℓ is a positive integer. The optimal α-pebbling number f_α^′(G) of G is the minimum number of pebbles used in an α-pebbling of G. We denote f_α^′(G) = f_ℓ^′(G) if α(v) = ℓ for each v ∈ V (G). The optimal pebbling number of a graph G is the optimal 1- pebbling number of G and denoted by f^′(G). In this paper, we first find the optimal 2-pebbling numbers and optimal 3-pebbling numbers of the cycle graph C_n. Second, we find the upper bound and lower bound of Cn. Lastly apply them to aproach optimal ℓ-Pebbling of C_n.

Keywords: optimal pebbling number, cycle.

A study of bull-design

Shu-Wen Lo ( )

Department of Mathematics, Tamkang University ( ⼤學數學 ) Advisor: Chin-Mei Kau Fu( )

A complete graph K_n is a simple graph of order n whose vertices are pairwise adjacent. A decomposition of graph G is a collection H = {H1, H₂, . . . , H_k} of subgraphs of G, such that E(H_i)∩ E(Hj) = ∅ (i ̸= j) and E(H1)∪ E(H2)∪ · · · ∪ E(H_k) = E(G). Let H be a graph, an H-design of a complete graph K_n, denoted by (K_n, H), is a pair (X,B), where X is the vertex set of the complete graph Kn and B

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is a collection of subgraphs of K_n, called blocks, such that each block is isomorphic to H, and any edge of K_n is contained in exactly one subgraph of K_n. Furthermore, G has an H-decomposition or G can be decomposed into H, if H_i is isomorphic to H (1≤ i ≤ k). Therefore, a (Kn, H)-design exists means K_n has an H-decomposition.

A bull is a graph B which is obtained by attaching two edges to two vertices of a triangle. A (K_n,B)-design is called a bull-design of order n.

In Chapter 2, we show that the necessary and suﬃcient condition of a bull-design of order n exist precisely when n≡ 0, 1 (mod 5).

In Chapter 3, we consider the maximum packing of bull-design of order n. We obtain that the leave of maximum packing is a set of one edge if n≡ 2 or 4 (mod 5) and a set of three edges if n ≡ 3 (mod 5). By the above results, we obtain that the necessary and suﬃcient conditions for the existence of bull-designs of a complete multi-partite graph λK_n are the follows: λ ̸≡ 0 (mod 5) and n ≡ 0, 1 (mod 5), or λ≡ 0 (mod 5) and for all n.

In Chapter 4, we obtain that the spectrum of bull-design of order n intersecting in pairwise disjoint blocks is 0, 1, 2, . . . , [n/5], when n > 5 and n≡ 0, 1 (mod 5), and the spectrum of bull-design of order 5 intersecting in pairwise disjoint blocks is 0.

We also show that the spectrum of triangle intersection numbers of two bull-design of order n is 0, 1, 2, . . . , n(n− 1)/10, for n ≡ 0, 1 (mod 5).

In Chapter 5, we obtain that a bull-design of order n can be embedded in a bull-design of order m if and only if m ≥ 3n/2 + 1 or m = n. This produces a generalization of the Doyen-Wilson theorem for bull-designs.

Keywords: Decomposition, bull-design, Packing, Intersection, Doyen-Wilson theorem.

A General Framework for Central Limit Theorems of Additive Shape Parameters in Random Digital

Trees

Chung-Kuei Lee ( )

National Chiao Tung University ( ⼤學數 )

Tries, PATRICIA tries and (bucket) Digital Search Trees are fundamental data structures in computer science with numerous applications. In recent papers, a

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general framework for obtaining the mean and variance of additive shape parameters of tries, PATRICIA tries and DSTs under the Bernoulli model was proposed. Later on, we showed that a slight modification of the frameworks yields a central limit theorem for shape parameters, too. This central limit theorem contains many of the previous central limit theorems from the literature and it can be used to prove recent conjectures and derive new results. As an example of the trie case, we will consider a refinement of the size of tries and PATRICIA tries, namely, the number of nodes of fixed outdegree and obtain (univariate and bivariate) central limit theorems. For the DSTs case, we use 2-protected node as an example to illustrate how the framework will work.

Spectral Excess Theorem and its Applications

Guang-Siang Lee ( )

National Chiao Tung University ( ⼤學數 ) Advisor: Chih-wen Weng( )

The spectral excess theorem gives a quasi-spectral characterization for a regular graph to be distance-regular. An example demonstrates that this theorem cannot directly apply to nonregular graphs. In order to make it applicable to nonregular graphs, a ‘weighted’ version of the spectral excess theorem is given. For application, we show that a graph with odd-girth 2d + 1 is distance-regular, generalizing a result of van Dam and Haemers. We then apply this line of study to the class of bipartite graphs. It is well-known that the halved graphs of a bipartite distance-regular graph are distance-regular. Examples are given to show that the converse does not hold.

Thus, a natural question is to ﬁnd out when the converse is true. We give a quasi- spectral characterization of a connected bipartite weighted 2-punctually distance- regular graph whose halved graphs are distance-regular. In the case the spectral diameter is even we show that the graph characterized above is distance-regular.

Keywords: Distance-regular graph, Distance matrices, Predistance polynomials, Spectral diameter, Spectral excess theorem.

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Covering Problems in Graphs

Sheng-Hua Chen ( )

Department of Mathematics, National Taiwan University ( ⼤學數學 ) Advisor: Gerard Jennhwa Chang( )

Covering problems in graphs are optimization problems about covering the vertex set V (G) or the edge set E(G) of a graph G under some additional restrictions. In other words, a graph covering of G is a collection of vertex/edge subsets of G such that each vertex or each edge of G is belonged to at least one subset in this collection.

Graph covering enjoys many practical applications as well as theoretical challenges. It is heavily used in various ﬁelds such as biochemistry (genomics), electrical engineering (communication networks and coding theory), computer science (algorithms and computation) and operations research (scheduling) etc.

In this thesis, we study six covering problems in graphs, which study the optimally of the following related functions. A strong edge-coloring is a function that assigns to each edge a color such that any two edges within distance two apart receive different colors. An edge Roman dominating function is the edge version of a Roman dominating function, that is, a function f : E(G)→ {0, 1, 2} such that every edge e with f (e) = 0 is adjacent to some edge e^′ with f (e^′) = 2. More generally, for a fixed positive integer k, a k-power Roman dominating function is a function f : V (G)→ {0, 1, . . . , k} such that every vertex u with f(u) = 0 is adjacent to some vertex v with f (v) = i≤ k within distance i. A distance edge cover is a generalization of an edge cover, that assigns each edge a label such that every vertex is within distance j from some edge with label j. A modular orientation is an orientation of edges such that the in-degree equals to the out-degree of each vertex. A relaxation procedure is a series of relabeling by changing the sign of a negative vertex and sharing the difference equally to its neighbors.

The purpose of this thesis is to study the above mentioned graph covering problems from algorithmic, algebraic and probabilistic point of view. In particular, we give exact values and/or upper/lower bounds for related parameters of these problems. New technics are developed to established interesting results, including the proofs/dis-proofs of some known conjectures.

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碩⼠

The 3-split of multipaths and multicycles with multiplicity 2

Meng-Ping Hsieh ( )

National Central University ( ⼤學數學 ) Advisor: Chiang Lin( )

Let G be a graph and t be a positive integer. A t-split of G is a partition of the edges of G into t isomorphic subgraphs. A graph is said to be t-splittable if it has a t-split.

In this thesis we prove the following results.

Theorem. Let Q be a multipath with multiplicity 2 such that |E(Q)|=0 (mod 3).

Then Q is 3-splittable.

Theorem. Let C be a multicycle with multiplicity 2 such that |E(C)|=0 (mod 3).

Then C is 3-splittable.

Diﬀy Hexagons

Wei-Ming Wang ( )

Department of Mathematical Science, National Chengchi University ( ⼤學數 )

Advisor: Young-Ming Chen( )

In this thesis, we study the Diﬀy Hexagons: Initially, we regard a Ducci sequence as a Diﬀy Hexagon game and discuss some properties about Ducci sequences.

However, a Ducci sequence isn’t actually a Diffy Hexagon game due to the fact that regular hexagons has some symmetries under rotations and reflections, but the Ducci sequences don’t. Therefore, we apply an identification in the end.

Keywords: Cycles, Diﬀy Hexagons, Ducci processes, Ducci sequences, Periods, Similar cycles.

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On the distribution of the leading statistic for the bounded deviated permutations

Wei-Liang Chien ( )

National Taiwan Normal University ( ⼤學數學 ) Advisor: Yen-Chi R. Lin( )

The purpose of the thesis is to investigate the distribution of the initial number in the bounded deviated permutations S_n+1^ℓ,r , assuming the uniform distribution in S_n+1^ℓ,r .

Define the random variable X_nto take the value k if π₁ = k+1 π = π₁π₂· · · πn+1∈ S_n+1^ℓ,r . By considering the bivariate generating function A(z, u), we could calculate the expected value and the standard deviation for X_n. The method is then applied to two specific cases, S_n+1^1,2 and S_n+1^2,2 . Since the coefficients λ_n,k of the bivariate generating function do not have a closed form, we will apply the Hayman method to get its asymptotic formula. Finally, by running computer programs, the convegences of the normal distribution of S_n+1^1,2 and S_n+1^2,2 are verified.

The Number of 2-Protected Nodes in Tries and PATRICIA Tries

Guan-Ru Yu ( )

National Chiao Tung University ( ⼤學數 ) Advisor: Michael Fuchs( )

Digital trees are data structures which are of fundamental importance in Com- puter Science. Recently, so-called 2-protected nodes have attracted a lot of attention.

For instance, J. Gaither, Y. Homma, M. Sellke, and M. D. Ward derived an asymptotic expansion for the mean of the number of 2-protected nodes in random tries.

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Moreover, J. Gaither and M. D. Ward considered the variance and conjectured a central limit theorem.

In this talk, we will explain our recent results on the number of 2-protected nodes in tries and PATRICIA tries. More precisely, we will derive asymptotic expansions of moments and prove the conjectured central limit theorem of J. Gaither and M.

D. Ward. An interesting aspect of our work is that our results contain divergent series which however become convergent (and yield correct results) by appealing to the theory of Abel summability.

Keywords: digital tree, 2-protected nodes, moments, central limit theorem.

Perfect Secret Sharing Schemes for Access Structures Based on Graphs

Bo-Rong Lin ( )

National Chiao Tung University ( ⼤學數 ) Advisor: Hung-Lin Fu( ) and Hui-Chuan Lu( )

A perfect secret sharing scheme based on a graph G is a randomized distribution of a secret among the vertices of the graph so that the secret can be recovered from the information assigned to the endvertices of any edge, while the total information assigned to an independent set of vertices is independent (in statistical sense) of the secret itself.

The (worst case) information ratio of G is the largest lower bound on the amount of information some vertex must remember for each bit of the secret. Using entropy method, we calculate a lower bound on the information ratio for an inﬁnite class of graphs we consider in this thesis. We also use the generalized vector space construction to construct perfect secret sharing schemes with information ratio 2 for two subclasses of graphs. This upper bounded is very close to our lower bound in some circumstances, which means the secret sharing schemes we construct are in fact very good.

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A Study on Quality-Enhanced Visual Multi-Secret Images Sharing Schemes

Lu-Chung Chen ( )

Department of Computer Science and Information Engineering, National Chi Nan University ( ⼤學程學 )

Advisor: Justie Su-Tzu Juan ( )

Visual secret sharing is a method of encrypting images. In 2012, a multiple visual secret sharing scheme by shifting random grid was proposed by Chang. In this scheme, multiple secret-images can be encrypted into two share images. However, the distortion of this scheme is quite high (especially when the number of secret images are more). In order to decrease the distortion of this scheme, we propose three improved multiple visual secret sharing schemes by shifting random grid.

The ﬁrst method of our schemes is increasing the number of fragments (INF, for short). The second is increasing the number of shares (INS, for short). The third is distributing the black pixels evenly on shares (DBPEOS, for short), this method not decreases the quantity of distortion but increases the evenness of black pixels.

In addition to less distortion, INS develops two new modes for mobile devices.

Therefore, our proposed schemes can be used for more applications.

Keywords: visual secret sharing, random grid, multiple secret-images, mobile devices.

The Minimum Rank of Buds

Po-Yu Hsu ( 博 )

National Chiao Tung University ( ⼤學數 ) Advisor: Chih-Wen Weng( )

For a simple graph G of order n with vertex set [n] = {1, 2, · · · , n}, an n × n real symmetric matrix A, whose ij-th entry is not zero if and only if there is an edge joined i and j in G, is said to be associated with G. The minimum rank of G is deﬁned to be the smallest possible rank over all symmetric real matrices associated

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with G. A bud based on [n− m] is a graph G with vertex set V (G) = [n] satisfying the following axioms:

(i) The subgraph of G induced on [n − m] is a cycle Cn−m, and the subgraph induced on [n]\ [n − m] has no edge.

(ii) The cycle C_n_−m can be parted into m disjoints paths, and the length of these paths are at least 2. For all vertex v in [n]\ [n − m], v has at least three neighbors in the same path. Any two vertices in [n]\ [n − m] are not connected to the same path.

In the thesis we will show that a bud based on [n− m] has minimum rank n − m − 2.

Keywords: Graph, Minimum rank, Bud.

Mathematical Properties and Construction of Quantum Error Correcting Codes

Jui-Yi, Tsai ( )

This thesis introduces about the quantum error correcting codes in the viewpoint of classical error correcting codes. We also introduce some construction and characterization of quantum error correcting codes. Thereafter, we give a construction of quantum error correcting codes associated with graphs, which generalizes a previous result that excludes the binary case so that it is valid for all cases.

Keywords: quantum error correcting codes,graph.

The study of r-locating-dominating codes in paths

Hsiao-Yun Lin ( )

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National Sun Yat-sen University ( ⼤學數 ) Advisor: Li-Da Tong( ⼤)

The locating-dominating code of graph was introduced by Colbourn, Slater, and Stewart. Slater proved that M₁^LD(Pn) = ⌈²ⁿ₅ ⌉. Honkaia proved that M2^LD(Pn) =

⌈ⁿ⁺¹₃ ⌉. Exoo, Junnila, and Laihonen determined Mr^LD(P_n) for (3 ≤ r ≤ 4) and (r ≥ 5 and 2 ≤ n ≤ 7r + 3). In this thesis, we determine M_r^LD(P_n) for r ≥ 5 and 7r + 4≤ n ≤ 11r + 5.

Keywords: Locating-dominating code, Dominating, Graph.

The study of secure-dominating set of graph products

Hung-Ming Chang ( )

National Kaohsiung Normal University ( ⼤學數學 ) Advisor: Hsin-Hao Lai( )

If G is a graph and v is a vertex of G, then N_G(v) denotes the neighborhood of v in G and N_G[v] denotes the closed neighborhood of v in G. Given a subset S of V (G), a function A deﬁned on S is called an attack on S in G if A(u)⊆ NG(u)− S for any u ∈ S and A(u) ∩ A(v) = ∅ for any distinct vertices u, v. And a function D deﬁned on S is called a defense of S if D(u) ⊆ NG[u]∩ S for any u ∈ S and D(u)∩ D(v) = ∅ for any distinct vertices u, v. A nonempty subset S of V (G) is called a secure set of G if for each attack A on S, there exists a defense of S such that |D(u)| ≥ |A(u)| for any u ∈ S.

One can think the vertices of A(u) as attackers of u and those of D(u) as defenders of u. Each vertex not in S can attack at most one of its neighbor in S. And each vertex in S can defense at most one attack on itself or one attack on its neighbors in S. The attack is thwarted if |D(u)| ≥ |A(u)|. For a secure set S, each attack on S can be thwarted.

A set S is a secure-dominating set of G if S is a secure set of G that is also a dominating set of G. The secure-dominating number of G is the minimum cardinality of secure-dominating sets of G.

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In this thesis, we obtain some results of secure-dominating sets and secure- dominating numbers of strong product and lexicographic product of graphs.

Keywords: secure-dominating set, secure-dominating number, strong product, lexicographic product.

The Laplacian Spectral Radius of a Graph

Fan-Hsuan Lin ( )

Let G = (V, E) be a simple connected graph with the vertex set V and the edge set E. We have a new sharp bound for the Laplacian spectral radius of G, which improves some known upper bounds.

Keywords: Graph, Laplacian matrix, Laplacian spectral radius.

Error-correcting pooling designs and group testing for consecutive positives

Yi-Tsz Tsai ( )

National University of Kaohsiung ( ⼤學數 ) Advisor: Huilan Chang( )

Pooling designs are standard experimental tools in many biotechnical applications. Many famous pooling designs have been constructed from mathematical structures by “containing relation”. Recently, pooling designs constructed by “intersecting relation” have been proposed by Nan and Guo (2010) and Guo and Wang (2011). Constructing by intersecting relation provides much better error-tolerance capabilities. In this thesis, we study the error-tolerance capabilities of pooling designs constructed by intersecting relation from combinatorial structures proposed by

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D’yachkov et al. (2007) and Bai et al. (2009). Motivated by application to DNA sequencing, group testing for consecutive positives has been proposed by Balding and Torney(1997) and Colbourn (1999) where n items are linearly ordered and all up to d positive items are consecutive in the order. In this thesis, we study a vari- ation of (k, m, n)-selectors and use this combinatorial object to design a two-stage algorithm for group testing of consecutive positives. Our algorithm takes at most 12 log₂⌈n/d⌉ + 14e + 3d tests to identify all positives and its decoding complexity is O(ⁿ_dlogⁿ_d+ d).

Keywords: Group Testing, Pooling design, Error-tolerance, Consecutive Posi- tives.

Threshold group testing with consecutive positives

Yi-Lin Tsai ( )

National University of Kaohsiung ( ⼤學數 ) Advisor: Huilan Chang( )

Threshold group testing introduced by Damaschke (2006) is a generalization of classical group testing where a group test yields a positive (negative) outcome if it contains at least u (at most l) positive items, and an arbitrary outcome for other- wise. Motivated by applications to DNA sequencing, group testing with consecutive positives has been proposed by Balding and Torney (1997) and Colbourn (1999) where n items are linearly ordered and all up to d positive items are consecutive in the order. In this thesis, we use threshold-constrained group tests to deal with group testing with consecutive positives. We prove that all positive items can be identiﬁed in⌈log2(⌈n/u⌉ − 1)⌉ + 2⌈log2(u + 2)⌉ + ⌈log2(d− u + 1)⌉ − 2 tests sequen- tially for the gap-free case (u = l + 1) while the information-theoretic lower bound is ⌈log2n(d− u + 1)⌉ − 1 when n ≥ d + u − 2 and show that the case with a gap (u > l + 1) can be dealt with by the subroutines used to conquer the gap-free case.

Using a variation of cover-free family we show that the set of positives can be approx- imately identiﬁed in 15 log₂ ⁿ_d + 4d + 71 group tests nonadaptively and its decoding complexity is O(ⁿ_dlog₂ ⁿ_d+ ud²).

Keywords: Group testing, Threshold, Consecutive positives, Cover-free families.

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Weight Choosability of theta Graphs

Ting-Feng Jian ( )

National Taiwan University ( ⼤學數學 ) Advisor: Gerard Jennhwa Chang( )

The 1,2,3-conjecture is a problem of edge weight colorability of graphs which was posed by M. Karoński et al in 2004. Further problem of edge weight choosability of graphs was posed by T. Bartnicki et al in 2009. While being solved for some special cases, the two problems are still open nowadays. In this thesis, we use the combinatorial nullstellensatz and the permanent to ﬁnd some results. We go through the cycles, then discuss the θ-graphs and generalized θ-graphs. The main result of this thesis is to show these graphs are all 3-edge weight choosable.

Keywords: weight choosability, 3-weight choosable, combinatorial nullstellen- satz, permanent, cycles, θ-graphs, generalized θ-graphs.

On Antimagic Labeling and Associated Deﬁciency Problems for Graph Products

Si-Hao Wu ( )

National Chiao Tung University ( ⼤學數 ) Advisor: Hung-Lin Fu( ) and Tao-Ming Wang( )

Let G = (V (G), E(G)) be a finite simple graph with p = |V (G)| vertices and q = |E(G)| edges. An antimagic labeling of G is a bijection from the set of edges to the set of integers {1, 2, · · · , q} such that the vertex sums are pairwise distinct, where the vertex sum at a vertex is the sum of labels of all edges inci- dent to such vertex. Moreover G is called (a, d)-antimagic if the vertex sums are a, a + d,· · · , a + (|V | − 1)d for some positive integers a and d. For the graph G, the (a, d)-antimagic deficiency (antimagic deficiency, respectively) is defined as the minimum integer k such that the injective edge labeling f : E(G)→ {1, 2, · · · , q +k}

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is (a, d)-antimagic (antimagic, respectively). This thesis mainly studies antimagic la- belings and associated antimagic deficiency problems for certain graph products. In particular, we show the antimagic-ness for strong product of any even regular graph and any regular graph. Also we determine the (a, 1)-antimagic deficiency for the Cartesian product of cycles C_m₁Cm2 and the (a, 1)-antimagic deficiency for the strong product of cycles C_m₁ Cm2.

Keywords: antimagic labeling, antimagic graph, strong product, Cartesian product.

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附錄

陳聖華 (臺大數學) 羅淑玟 (淡江數學) 李忠逵 (交大應數) 連敏筠 (交大應數) 李光祥 (交大應數) 邱鈺傑 (交大應數)

梁育菖 (中山應數)(103.2) 林哲宇 (中山應數)(103.2) 廖芳儀 (中原應數)(103.2)

榮獲博士學位

張宏名 (高師數學) 簡維良 (台師數學) 王偉名 (政大應數) 林筱芸 (中山應數) 簡廷豐 (臺大數學) 蔡睿翊 (交大應數) 余冠儒 (交大應數) 許博喻 (交大應數) 林凡軒 (交大應數) 鄭伊婕 (交大應數) 林伯融 (交大應數) 吳熹皓 (交大應數) 謝孟萍 (中央數學) 蔡宜霖 (高大應數) 蔡一慈 (高大應數) 陳律仲 (暨大資工)

榮獲碩士學位

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會

⼤會演講

E-mail

研數學 makwlih@sinica.edu.tw

⼤學數學 lchiang@math.ncu.edu.tw

⼤學數 tlwong@math.nsysu.edu.tw

⼤⼤學數 ldtong@math.nsysu.edu.tw

⼤學數學 cyshen@math.ncu.edu.tw

⼤學數學 scliaw@math.ncu.edu.tw

⼤學數學 clshiue@math.cycu.edu.tw

⼤學數學 bytsai0808@gmail.com

⼤學 jungle@cute.edu.tw

⼤學 yp-tsao@gm.cute.edu.tw

⼤學數 weitianli@dragon.nchu.edu.tw

⼤學數 yltsai@nchu.edu.tw

mingju99@jente.edu.tw

⼤ mhhuang@mail.ypu.edu.tw

⼤學數學 gjchang@math.ntu.edu.tw

⼤學數學 twhsu@ntnu.edu.tw

⼤學數學 feihuang0228@gmail.com

⼤學數學 yclinpa@gmail.com

⼤學數學 junyiguo@gmail.com

⼤學數學 senpengeu@gmail.com

⼤學數學 wuhsiunglin@nctu.edu.tw

⼤學數學 mfuchs@math.nctu.edu.tw

⼤學數學 cychen@mail.nctu.edu.tw

⼤學數學 hlfu@math.nctu.edu.tw

⼤學數學 pyhuang@mail.ncku.edu.tw

⼤⼤學數學 davidk@mail.ndhu.edu.tw

⼤學 tsfu@npic.edu.tw

⼤學數學 deed@math.nccu.edu.tw

⼤學數學 zhabiz@gmail.com

⼤學數學 au4088@mail.au.edu.tw

⼤學數學 huilan0102@gmail.com

⼤學數學 hsinhaolai@nknucc.nknu.edu.tw

⼤學 jsjuan@ncnu.edu.tw

⼤學數學 cmfu@mail.tku.edu.tw

⼤學數學 zhishi.pan@gmail.com

chaomingsun@gmail.com

⼤學 jlshang@mail.knu.edu.tw

⼤學數學 jackjunjiepan@gmai.com

⼤學 yllai@mail.ncyu.edu.tw

⼤學數 chyen@mail.ncyu.edu.tw

⼤學數學 kchuang@gm.pu.edu.tw

⼤學 jjlin@teamail.ltu.edu.tw

⼤學 birdy@teamail.ltu.edu.tw

⼤學 mjjou@teamail.ltu.edu.tw

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E-mail

研學研數學 andanchen@gmail.com

博⼠研⼤學數學 huiqiulin@126.com

博⼠研⼤學數學 yenpl.tw@gmail.com

博⼠研⼤學數學 hchsu0222@gmail.com

博⼠研研 gaussla@gmail.com

博⼠研研數學 fyliao920@gmail.com

博⼠研⼤學數學 owlerson@yahoo.com.tw

博⼠研⼤學數學 yphuang@isu.edu.tw

博⼠⼤學數

博⼠⼤學數學 tremolo.am96g@nctu.edu.tw

博⼠⼤學數學 enix45@gmail.com

博⼠⼤學數學 well.am94g@nctu.edu.tw

博⼠⼤學數學 lienmy.am94g@nctu.edu.tw

博⼠⼤學 shuwen4477@yahoo.com.tw

博⼠⼤學數學 r95221034@ntu.edu.tw

學博⼠⼤學數學 zzuedujinyalei@163.com

學博⼠⼤學數學 jinyu.97@gmail.com

學博⼠⼤學數學 amco0624@yahoo.com.tw

學博⼠⼤學數學 ji3chinima@gmail.com

學博⼠⼤學 lu@math.cm.is.nagoya-u.ac.jp

學博⼠⼤學數學 jackhu@ntnu.edu.tw

學博⼠⼤學數學 yjc7755@gmail.com

學博⼠⼤學 810111001@ems.ndhu.edu.tw

學博⼠⼤學數學 jazztct@yahoo.com.tw

學博⼠⼤學 chlin@iastate.edu

學博⼠⼤學程學 s96321901@gmail.com

碩⼠⼤學數學 feel_1103@yahoo.com.tw

碩⼠⼤學 hmengping@gmail.com

碩⼠⼤學數學 jason32338@hotmail.com

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研討會

21 2014.8.2–3 ⼤學數學組合數學新苗研討會

19 2012.8.10–12 ⼤學數學組合研討會組合數學新苗研討會

17 2010.8.7–8 研數學研組合數學新苗研討會

14 2007.8.10–11 ⼤學數學組合數學 (新苗) 研討會

13 2006.8.11–12 ⼤學新組合數學研討會

12 2005.8.26–27 ⼤學數學組合數學研討會

11 2004.8.27–28 ⼤學數學組合數學研討會

10 2003.9.5–6 ⼤學數學組合數學研討會

7 2000.6.16 ⼤學數學組合數學新苗研討會

6 1999.6.11–12 研數學組合數學新苗研討會

4 1997.6.27–28 ⼤學數學組合數學研討會

3 1996.5.24–25 ⼤學數學組合數學研討會

1 1990.6.25–26 研數學研數學新苗研討會

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Memo

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⼤學數學

2014 組合數學新苗研討會

⼤學數學

2014 8 2 3

⼤會演講

李國偉 教授 中央研究院

林強 教授 中央大學數學系

台灣師範大學公館校區 科教大樓 5 樓演講廳

科技部自然司數學研究推動中心

國家理論科學研究中心數學組 (臺北辦公室) 東賢實業股份有限公司

游森棚 (台灣師範大學數學系)

林延輯 (台灣師範大學數學系)

郭君逸 (台灣師範大學數學系)

徐泰煒 (台灣師範大學僑先部)

張飛黃 (台灣師範大學僑先部)

⼤會宗旨

新苗

Contents

2014 組合數學新苗研討會議程

⼤會演講

Graph Labellings: Splittable Graphs and Antimagic Graphs

Chiang Lin ( )

Rota’s Lessons

Ko-Wei Lih ( )

邀請演講

Lovász Local Lemma, Entropy Compression and Graph Colorings

Hsin-Hao Lai ( )

Reference

Which connected graphs are determined by their distance spectra

Huiqiu Lin ( )

The spectral radius of connected graphs with the independence number *

Ya-Lei Jin ( )

On aﬃne-invariant strictly cyclic Steiner quadruple systems

Xiao-Nan Lu ( )

博⼠

Maximum packings and minimum coverings of multigraphs with paths and stars

Chun-Cheng Chen ( )

Factorizations of Suﬃxes of Two-Way Inﬁnite Characteristic Words

Fang-Yi Liao ( )

Self-stabilizing Minimal Dominating Set Algorithms of Distributed Systems and the Signed Star Domination Number

of Cayley Graphs

Well Y. Chiu ( )

Decycling Number on Graphs and Digraphs

Min-Yun Lien ( )

Optimally ℓ-Pebbling Cycles

H. X. Chiang ( )

A study of bull-design

Shu-Wen Lo ( )

A General Framework for Central Limit Theorems of Additive Shape Parameters in Random Digital

Trees

Chung-Kuei Lee ( )

Spectral Excess Theorem and its Applications

Guang-Siang Lee ( )

Covering Problems in Graphs

Sheng-Hua Chen ( )

碩⼠

The 3-split of multipaths and multicycles with multiplicity 2

Meng-Ping Hsieh ( )

Diﬀy Hexagons

Wei-Ming Wang ( )

On the distribution of the leading statistic for the bounded deviated permutations

Wei-Liang Chien ( )

The Number of 2-Protected Nodes in Tries and PATRICIA Tries

Guan-Ru Yu ( )

Perfect Secret Sharing Schemes for Access Structures Based on Graphs

Bo-Rong Lin ( )

A Study on Quality-Enhanced Visual Multi-Secret Images Sharing Schemes

Lu-Chung Chen ( )

The Minimum Rank of Buds

Po-Yu Hsu ( 博 )

Mathematical Properties and Construction of Quantum Error Correcting Codes

Jui-Yi, Tsai ( )

The study of r-locating-dominating codes in paths

Hsiao-Yun Lin ( )

The study of secure-dominating set of graph products

Hung-Ming Chang ( )

The Laplacian Spectral Radius of a Graph

Fan-Hsuan Lin ( )

Error-correcting pooling designs and group testing for consecutive positives

Yi-Tsz Tsai ( )

李國偉教授中央研究院

林強教授中央大學數學系

台灣師範大學公館校區科教大樓 5 樓演講廳

The spectral radius of connected graphs with the independence number ^*