给定割点数的单圈图的第二大谱半径

The Second Largest Spectral Radii of Unicyclic Graphs with Fixed Number of Cut Vertices

谱图理论的一个主要问题是研究图的结构性质如何由图的谱性质反映.割点数是图的重要结构参数,讨论了单圈图的割点数和谱半径之间的联系.在刻画了给定割点数的单圈图中具有最大谱半径图的结构基础上,延续这一讨论,刻画了在某些情形下,给定割点数的单圈图中具有第二大谱半径的图的结构.

It is the main problem in spectral graph theory to discuss how the structural property of a graph is characterized by its spectral property.The number of cut vertices is an important structural parameter of graphs.This paper discuss the relations between the number of cut vertices and spectral radii of unicyclic graphs.In other conference,the graph with maximum spectral radius among all the unicyclic graphs with fixed number of cut vertices is determined.In this paper,we continue this work and characterize the graph with second largest spectral radius among all unicyclic graphs with fixed number of cut vertices in some cases.