含偶圈图的Laplacian谱刻画  

Laplacian spectral characterizations of graphs with even cyclic

作　　者：丁超 余桂东 DING Chao;YU Guidong(School of Mathematics and Computation Sciences,Anqing Normal University,Anqing 246133,Anhui,China;Basic Department,Hefei Preschool Education College,Hefei 230013,China)

机构地区：[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

出　　处：《运筹学学报》2018年第4期135-140,共6页Operations Research Transactions

基　　金：安徽省高等学校自然科学基金(Nos.KJ2015ZD27;KJ2017A362)

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.Let H(K1,5,Pn,Cl) be a unicyclic graph obtained from a path Pn by attaching a star K1,5 and a cyclic Cl 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(K1,5,Pn,C4), H(K1,5,Pn,C6)are determined by their Laplacian spectra.

关 键 词：LAPLACIAN谱 线图 邻接谱 偶圈 

分 类 号：O151.21[理学—数学] O157.5[理学—基础数学]