圈长和顶点数给定的单圈图的Laplace 谱半径排序

Ordering of Unicyclic Graphs with Cycle Length g and Vertices n

摘要:

只含一个圈的简单连通图称为单圈图.郭继明给出了固定圈长的单圈图的 Laplace 谱半径并刻画了相应的极图.该文在此基础上确定了圈长为g的所有n=g+k(g≥5,k≥3)阶单圈图的Laplace 谱半径从大到小的前［g/2］个图.

关键词:单圈图; Laplace 矩阵; Laplace 谱半径; 特征多项式

Abstract:

A unicyclic graph is either a cycle or a cycle with trees attached. GUO Jiming gave the first largest Laplacian spectral radius among all unicyclic graphs with cycle length g and n vertices. In this paper,the first largest ［g/2］graphs is determined according to Laplacian spectral radii among all unicyclic graphs with cycle length g and n=g+k(g≥5,k≥3) vertices.

Key words:unicyclic graph; Laplace matrix; Laplacian spectral radius; characteristic polynomial