广义边冠图的Normalized Laplacian谱

The Normalized Laplacian Spectra of the Generalized Edge Corona of Graphs

设G和H_1,H_2,…,H_m是简单图,其中G的边数为m.对每一个i∈{1,2,…,m},把G的第i条边的每一个顶点与Hi的每一个顶点相连,得到的图记为G[Hi]_1~m,称为由G和H_1,H_2,…,H_m得到的广义边冠图.主要研究了G[Hi]_1~m的normalized Laplacian谱,计算了G[Hi]_1~m的degree-Kirchhoff指标和生成树的数目.

Let G and H 1,H 2,…,H m be simple graphs,where G contains m edges.For each i∈{1,2,…,m},we join edges between two end-vertices of the i′th edge of G and each vertex of H i,and obtain a new graph,denoted by G[H i]m 1,which is called to be the generalized edge corona of G and H 1,H 2,…,H m.In this paper,we determine the normalized Laplacian spectrum of G[H i]m 1.For applications,the degree-Kirchhoff index and the number of spanning trees of G[H i]m 1 are considered.