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含偶圈图的Laplacian 谱刻画

丁超1,*  余桂东1,2   

  1. 1. 安庆师范大学数学与计算科学学院, 安徽安庆 246133; 2. 合肥幼儿师范高等专科学校基础部, 合肥 230013
  • 收稿日期:2017-07-31 出版日期:2018-12-15 发布日期:2018-12-15
  • 通讯作者: 丁超 E-mail: 75360143@qq.com
  • 基金资助:

    安徽省高等学校自然科学基金(Nos. KJ2015ZD27, KJ2017A362)

Laplacian spectral characterizations of graphs with even cyclic

DING Chao1,*  YU Guidong1,2   

  1. 1. School of Mathematics and Computation Sciences, Anqing Normal University, Anqing 246133, Anhui, China; 2. Basic Department, Hefei Preschool Education College, Hefei 230013,  China
  • Received:2017-07-31 Online:2018-12-15 Published:2018-12-15

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摘要：

设 H(K_{1,5},P_n,C_l)是由路 P_n的两个悬挂点分别粘上星图K_{1,5}的悬挂点和圈 C_l的点所得的单圈图. 若两个二部图是关于Laplacian 矩阵同谱的, 则它们的线图是邻接同谱的, 两个邻接同谱图含有相同数目的同长闭回路. 如果任何一个与图G关于Laplacian 同谱图都与图G 同构, 那么称图G可由其Laplacian 谱确定. 利用图与线图之间的关系证明了H(K_{1,5},P_n,C_4)、H(K_{1,5},P_n,C_6) 由它们的Laplacian谱确定.

关键词: Laplacian 谱, 线图, 邻接谱, 偶圈

Abstract:

Let H(K_{1,5},P_n,C_l) be a unicyclic graph obtained from a path P_n by attaching a star K_{1,5} and a cyclic C_l to its two pendent vertices respectively. If two bipartite graphs are Laplacian cospectral, then their line graphs are adjacency cospectral. The numbers of the same length walks are equal in two adjacency cospectral graphs. A graph G is called to be determined by its Laplacian spectrum if any graph having the same Laplacian spectrum as G is isomorphic to G.  Using the relation between graphs and line graphs, it is proved that the unicyclic graphs H(K_{1,5},P_n,C_4), H(K_{1,5},P_n,C_6) are determined by their Laplacian spectra.

Key words: Laplacian spactrum, line graph, adjacency spactrum, even cyclic