给定最大度的单圈偶图的谱半径  

On the spectral radii of unicyclic bipartite graphs with fixed maximum degree

作　　者：尹连伟[1,2] 郭曙光[1] 

机构地区：[1]盐城师范学院数学科学学院,江苏盐城224002 [2]江苏师范大学数学科学学院,江苏徐州224002

出　　处：《高校应用数学学报（A辑）》2013年第1期72-80,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11171290);江苏省自然科学基金(BK2010292)

摘　　要：单圈偶图是边数等于顶点数的简单连通偶图.Δ(G)表示图G的最大度.文中给出了最大度为Δ(≥^(n+1)/2)的n阶单圈偶图的谱半径的上界,并刻画了达到该上界的图.文中还证明了当Δ(G)≥[(2n+1)/3]+1时,n(≥8)阶单圈偶图G的谱半径随着最大度的递增而严格递增,并在此基础上给出了谱半径排在前17位的n(≥16)阶单圈偶图.A unicyclic bipartite graph is a connected bipartite graph in which the number of edges equals the number of vertices. Denote by △（G） the maximum degree of graph G. In this paper we determine the upper bound of spectral radii of unicyclic bipartite graphs on n vertices with fixed maximum degree A △（≥2/n＋1） and characterize the graph in which the maximal spectral radius is attained. We also prove that the spectral radius of a unicyclic bipartite graph G on n （≥ 8） vertices strictly increases with its maximum degree when △（G）≥「3/2n＋1」＋1. On this basis we give the first seventeen unicyclic bipartite graphs on n n（≥16） vertices according to the spectral radius.

关 键 词：单圈图 最大度 偶图 谱半径 

分 类 号：O157.5[理学—数学]