The Hamiltonian properties for faulty pancake graphs 梁高源、洪春男
E-mail: [email protected]
ABSTRACT
The use of pancake and star networks as an interconnection network has been studied by many researchers. The fault tolerance for Hamiltonian networks is also an important issue. In this thesis, we prove that an n-dimensional faulty pancake graph contains a Hamiltonian cycle with n-3 faults. (including faulty nodes and faulty edges). Furthermore, there exist Hamiltonian paths between two arbitrary but distinct nodes in a faulty pancake graph with n-4 faults. A graph G is a strongly k-Hamiltonian graph if "v ?( V-F ) there exist k+2-|F| edges incident to v such that every pair of these edges is on some Hamiltonian cycle of G-F, for all F ? (V?E) and |F| ? k. We also prove that the pancake graphs are strongly (n-3)-Hamiltonian graphs.
Keywords : pancake graph ; fault tolerance ; interconnection network ; k-Hamiltonian ; k-Hamiltonian connected ; strongly k-Hamiltonian
Table of Contents
Chapter 1 Introduction and definition………..1 Chapter 2 Pancake graphs are (n-3)-Hamiltonian and (n-4)- Hamiltonian connected………5 Chapter 3 Pancake graphs are strongly (n-3)-Hamiltonian……..18 3.1 Strongly
k-Hamiltonian graphs………..18 3.2 Pancake graph are strongly (n-3)-Hamiltonian…..20 Chapter 4 Conclusions ………
………24 Referance……… .25 REFERENCES
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