边剖分点冠图和边剖分边冠图的谱（英文）

Spectra of the Edge-Subdivision-Vertex and Edge-Subdivision-Edge Coronae

定义两个图G_1和G_2的冠图:边剖分点冠图G_1∨G_2和边剖分边冠图G_1G_2;并用原图的邻接谱、拉普拉斯谱、无符号拉普拉斯谱表示两类冠图的邻接谱、拉普拉斯谱、无符号拉普拉斯谱.基于拉普拉斯谱,给出并证明两类冠图G_1∨G_2和G_1G_2的生成树数目以及Kirchhoff指数.

In this paper two classes of corona are defined: edge-subdivision-vertex corona G_1∨G_2and edge-subdivision-edge corona G_1G_2. Then,the A-spectrum( respectively,L-spectrum,Q-spectrum) of the two classes of new graphs are given in terms of the corresponding spectra of G_1 and G_2. By using the Laplacian spectra,the number of spanning trees and Kirchhoff index of G_1∨G_2and G_1G_2are obtained.