单圈混合图的极大谱半径(英文)  

Maximizing Laplacian Spectral Radius over Unicyclic Mixed Graphs

作　　者：何江宏[1] 范益政[1] 

机构地区：[1]安徽大学数学科学学院,安徽合肥230039

出　　处：《大学数学》2008年第6期17-21,共5页College Mathematics

基　　金：National Natural Science Foundation of China(10601001);Anhui Provincial Natural Science Foundation(050460102);NSF of Depart ment of Education of Anhui Province(2004kj027,2005kj005zd);Foundation of Mathematical Innovation Teamof Anhui University,and Foundation of Talents Group Construction of Anhui University

摘　　要：设U*为一个未定向的n个顶点上的单圈混合图,它是由一个三角形在其某个顶点上附加n-3个悬挂边而获得.在文[Largest eigenvalue of a unicyclic mixed graph,Applied Mathematics A Journal of Chinese Universities(Ser.B),2004,19(2):140-148]中,作者证明了:在相差符号同构意下,在所有n个顶点上的单圈混合图中,U*是唯一的达到最大Laplace谱半径的混合图.本文应用非负矩阵的Perron向量,给出上述结论的一个简单的证明.Let U＊ be an unoriented unicyelic mixed graph on n vertices which is obtained from a triangle by appending n--3 pendent edges to one of its vertices. In the paper [Largest eigenvalue of a unicyclic mixed graph, Applied Mathematics A Journal of Chinese Universities （Ser. B）, 2004, 19 （2） ： 140 -- 148], the authors prove that up to signature isomorphisms U＊ is the unique graph which maximizes Laplacian spectral radius over all unicyclic mixed graphs on n vertices. In this paper, we use a simple method to prove above result by the Perron vectors of nonnegative matrices.

关 键 词：混合图 单圈图 LAPLACE谱半径 PERRON向量 

分 类 号：O157.5[理学—数学]