似双星树H(p,n,q)由Laplacian谱刻画

Double starlike tree H( p,n,q) determined by Laplacian spectrum

似双星树是恰好有两个结点的度大于2的树。用H(p,n,q)表示将路图Pn的两个悬挂点分别与星图S1,p及S1,q的中心点重合所得到的一类似双星树。首先得到了顶点的度序列,然后由谱性质证明了似双星树H(p,n,q)由Laplacian谱确定,扩大了谱确定图的范围。

A tree is called double starlike if it has exactly two vertices of degree greater than two. Let H（ p,n,q） denote a class of double starlike tree obtained from two stars S1,pand S1,qby identifying the center of S1,pwith one end of Pnand the center of S1,qwith the other end of Pn. First,we get the degree sequence of vertices. Then,by using spectral properties,it is proved that all double starlike trees H（ p,n,q） are determined by their Laplacian spectra,which enlarges the scope of graphs determined by their spectra.