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单圈混合图的极大谱半径
引用本文:何江宏,范益政.单圈混合图的极大谱半径[J].工科数学,2008(6):17-21.
作者姓名:何江宏  范益政
作者单位:安徽大学数学科学学院,安徽合肥230039
基金项目:Foundation item: National Natural Science Foundation of China (10601001); Anhui Provincial Natural Science Foundation (050460102) ; NSF of Department of Education of Anhui Province ( 2004kj027, 2005kj005zd) ; Foundation of Mathematical Innovation Team of 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”一3个悬挂边而获得.在文Largest eigenvalue of aunicyclic mixed graph,Applied Mathematics A Journal of Chinese Universities (Ser.B),2004,19(2):140-J48]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.

关 键 词:混合图  单圈图  Laplace谱半径  Perron向量

Maximizing Laplacian Spectral Radius over Unicyclic Mixed Graphs
HE Jiang-hong,FAN Yi-zheng.Maximizing Laplacian Spectral Radius over Unicyclic Mixed Graphs[J].Journal of Mathematics For Technology,2008(6):17-21.
Authors:HE Jiang-hong  FAN Yi-zheng
Institution:(School of Mathematial Science, Anhui University, Hefei Anhui 230039,China)
Abstract: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.
Keywords:mixed graph  unicyclic graph  Laplacian spectral radius  Perron vector
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