The Mutually Independent Hamiltonian Cycles of Chordal Rings

• Main Author: 謝勝宇
• Other Authors: 賴泳伶
• Format: Others
• Language: zh-TW
• Online Access: http://ndltd.ncl.edu.tw/handle/08763587546134868988

碩士 === 國立嘉義大學 === 資訊工程學系研究所 === 102 === Let G=(V,E) be a graph of order n. A Hamiltonian cycle of G is a cycle that contains every vertex in G. Two Hamiltonian cycles C1=<u1,u2,...,un,u1> and C2=<v1,v2,...,vn,v1> of G are independent if u1=v1 and ui=vi for 2<=i<=n. A set of Hamiltonian cycles {C1, C2,...,Ck} of G is mutually independent if its elements are pairwise independent. The mutually independent hamiltonicity IHC(G) of a graph G is the maximum cardinality of the set of mutually independent Hamiltonian cycle starting from any vertex of G. A chordal rings graph CR(n,d) is a graph with n vertices {0,1,2,...,n-1} and 2n edges such that vertex i is adjacent with vertices (i+1)(mod n) and (i+d)(mod n). This thesis considered the mutually independent hamiltonicity of chordal rings G and showed the sufficient and necessary condition for IHC(G)=4 .