第二大特征根不超过1的Cactus

On Cactuses Whose Second Largest Eigenvalue Does Not Exceed 1

图的第二大特征根与图的直径有着密切的联系,而图的直径对于网络研究有着非常重要的作用,因而研究图的第二大特征根有着很重要的实用价值。确定第二大特征根不超过1的图是图谱中著名的未解决问题,近年来人们得出了一系列关于第二大特征根不超过1的特殊简单图的结论。任意两个圈至多有一个公共顶点的简单连通图称为Cactus。运用找出禁用子图的方法给出了第二大特征根不超过1的所有Cactus。

The second largest eigenvalue of a graph is closely related to its diameter,and the diameter is very important for a network.Therefore,it is of great practical value to study the second largest eigenvalue of graphs.Determining all the graphs whose second largest eigenvalue does not exceed one is a well-known unsolved problem in spectra of graphs.In recent years,researchers determined serious special simple graphs whose second largest eigenvalue does not exceed one.The connected simple graph G is a cactus if any two of its cycles have at most one common vertex.The cactuses whose second largest eigenvalue dose not exceed one have been determined by forbidding subgraph.