图的能量与哈密尔顿性

运筹学学报 ›› 2014, Vol. 18 ›› Issue (2): 40-48.

图的能量与哈密尔顿性

余桂东^1,*, 张超¹, 龚奇娟¹

1. 安庆师范学院数学与计算科学学院, 安徽安庆, 246011

出版日期:2014-06-15 发布日期:2014-06-15
通讯作者: 余桂东 E-mail:yuguid@aqtc.edu.cn
基金资助:
国家自然科学基金(No. 11071002), 安徽省自然科学基金(No. 11040606M14), 安徽省高校自然科学基金(Nos. KJ2011A195, KJ2013A196), 安庆师范学院青年科学研究基金(No. KJ201307)

Energy and Hamiltonicity of graphs

YU Guidong^1,*, ZHANG Chao¹, GONG Qijuan¹

1. School of Mathematics and Computation Sciences, Anqing Normal University, Anqing 246011, Anhui, China

Online:2014-06-15 Published:2014-06-15

摘要/Abstract

摘要： 设G是一个无向简单图, A(G)为$G$的邻接矩阵. 用G的补图的特征值给出G包含哈密尔顿路、哈密尔顿圈以及哈密尔顿连通图的充分条件; 其次用二部图的拟补图的特征值给出二部图包含哈密尔顿圈的充分条件. 这些结果改进了一些已知的结果.

关键词: 图的能量, 哈密尔顿路, 哈密尔顿圈, 哈密尔顿连通图

Abstract: Let G be an undirected simple graph and A(G) be the adjacency matrix of G. This paper gives some sufficient conditions for G to have a Hamiltonian path or cycle or to be Hamilton-connected in terms of eigenvalues of the complement of G, and gives a sufficient condition for a bipartite graph to have Hamiltonian cycles in terms of eigenvalues of its quasi-complement. These results improve some known results.

Key words: energy of a graph, Hamiltonian path, Hamiltonian cycle, Hamilton-connected graph

中图分类号:

O157

余桂东, 张超, 龚奇娟. 图的能量与哈密尔顿性[J]. 运筹学学报, 2014, 18(2): 40-48.

YU Guidong, ZHANG Chao, GONG Qijuan. Energy and Hamiltonicity of graphs[J]. Operations Research Transactions, 2014, 18(2): 40-48.