一类新的整谱图

Some New Integral Graphs

设是一个简单的连通图,若的邻接矩阵的特征值全为整数,则称为整谱图.利用移接变形的方法,构造了一些新的整谱图.运用矩阵理论,证明了下列结论:若是由顶点为3的完全图通过复制次后,将其中每个图的一个顶点粘接在一起而成的图,这样具有个顶点.则是整谱图当且仅当i=k(k-1)/2,k∈Z+.

Let G be a simple connected graph with vertices,G is called integral graph if it has an integral spectrum.In the paper,using transplantation method,some new integral graphs have been constructed.We obtain the following result by matrix theory： Let K3 denote the complete graph on 3 vertices,let Gi（i=1,2…,n） denote the graph obtained by identifying the root u in i copies of K3.Then,Gi is an integral graph if and only if i=k（k-1）/2,k∈Z＋.