双圈图的Laplacian Spread(英文)  

The Laplacian Spread of Bicyclic Graphs

作　　者：刘颖[1] 王立庆[1] 

机构地区：[1]上海立信会计学院数学与信息学院,上海201620

出　　处：《数学进展》2011年第6期759-764,共6页Advances in Mathematics（China）

基　　金：Supported by the Natural Science Foundation of Shanghai(No11ZR1425100);the Innovation Program of Shanghai Municipal Education Commission(No11YZ241);Mathematics and Applied Mathematics by Special Fund of Shanghai(No1130IA15)

摘　　要：Laplacian spread的概念在刻画图的整体性质方面非常重要.近年来,Fan等分别刻画了树中具有极大和极小Laplacian spread的图.另外Bao等确定了在所有单圈图中具有极大Laplacian spread的图.边数减去顶点数目为1的连通图称为双圈图.令B_n是所有有n个顶点构成的双圈图集合.对n≥11,本文确定了B_n中所有具有极大Laplacian spread的那些图.The notion of Laplacian spread is very important in characterizing the global structural property of graphs. Recently, Fan et al. showed that K1,n-1 and Pn are the only trees with the maximal and the minimal Laplacian spread among all trees with n vertices, respectively. Furthermore, Bao etal. determined the graph with the maximal Laplacian spread among all unicyclic graphs. Connected graphs in which the number of edges equals the number of vertices plus one are called bicyclic graphs. Let Bn be the set of all bicyclic graphs with n vertices. In this paper, we continue the work on Laplacian spread of graphs, and determine those graphs with the maximal Laplacian spread in Bn for n≥11.

关 键 词：双圈图 LAPLACIAN SPREAD LAPLACIAN特征值 

分 类 号：O157.5[理学—数学]