关于三圈图的拉普拉斯谱半径的一些结果(英文)

Some Results on the Laplacian Spectral Radii of Tricyclic Graphs

边数等于点数加二的连通图称为三圈图.设△(G)和μ(G)分别表示图G的最大度和其拉普拉斯谱半径,设T(n)表示所有n阶三圈图的集合,证明了对于T(n)的两个图H_1和H_2,若△(H_1)>△(H_2)且△(H_1)≥n+7/2,则μ(H_1)>μ(H_2).作为该结论的应用,确定了T(n)(n≥9)中图的第七大至第十九大的拉普拉斯谱半径及其相应的极图.

A tricyclic graph is a connected graph in which the number of edges equals the number of vertices plus two.Let△（G） andμ（G） denote the maximum degree and the Laplacian spectral radius of a graph G,respectively.Let T（n） be the set of tricyclic graphs on n vertices.In this paper, it is proved that,for two graphs H_1 and H_2 in T（n）,if△（H_1）△（H_2） and△（H_1）≥（n＋7）/2,thenμ（H_1）μ（H_2）.As an application of this result,we determine the seventh to the nineteenth largest values of the Laplacian spectral radii among all the graphs in T（n）（n≥9） together with the corresponding graphs.