局部剖分邻接冠图的谱（英文）  

Spectra of Partially Subdivision Neighbourhood Coronae

作　　者：朱雪琴 田贵贤[1] 崔淑玉[2] 

机构地区：[1]浙江师范大学数理与信息工程学院,金华浙江321004 [2]浙江师范大学行知学院,金华浙江321004

出　　处：《数学进展》2017年第5期673-681,共9页Advances in Mathematics（China）

基　　金：Supported in part by NSFC(No.11371328);the Natural Science Foundation of Zhejiang Province(No.LY15A010011)

摘　　要：设G_1,G_2是两个简单连通图,图G_1,G_2的局部剖分邻接冠图G_1■G_2是指复制一个G_1和|V(G_1)|个G_2,图G_1的第i个点的邻点与复制的第i个图G2的每一个点相连接,然后在G_1每一条边上插入一个新的点而得到的图类.本文利用两个图G_1,G_2的邻接谱、Laplacian谱和无符号Laplacian谱刻画了局部剖分邻接冠图G_1■G_2的邻接谱、Laplacian谱和无符号Laplacian谱.另外,本文利用上述结果构造出了若干对邻接同谱图、Laplacian同谱图和无符号Laplacian同谱图.进一步地,本文也利用两个因子图G_1,G_2的Laplacian谱计算出了局部剖分邻接冠图G_1■G_2的生成树数目.Let G1, G2 be two simple connected graphs. The partially subdivision neigh- bourhood corona of G1 and G2, denoted by G1 ＊G2, is obtained by taking one copy of G1 and [V（G1）[ copies of G2, and joining the neighbours of the i-th vertex of G1 to every vertex in the i-th copy of G2, then inserting a new vertex into every edge of G1. In this paper, we determine the adjacency spectrum, Laplacian spectrum and signless Laplacian spectrum of G1 -G2 in terms of those of two factor graphs G1 and G2. In addition, as many applications of these results, we consider constructing infinite pairs of adjacency cospectral, Laplacian cospectral and signless Laplacian cospectral graphs. Moreover, we compute the number of spanning trees of G1 - G2 in terms of the Laplacian spectra of two factor graphs G1 and G2.

关 键 词：邻接矩阵 LAPLACIAN矩阵 无符号Laplacian矩阵 图的谱 局部剖分邻接冠图 

分 类 号：O157.5[理学—数学]