图Hn(Cp,Ps,K1,q)的Laplacian谱刻画

摘要

As a result of the discovery of the family of graphs, including the cycle Cp , path Ps and star graph K1 q, a new family of graphs have been defined and denoted by Hn ( Cp, Ps, K1 q) . These new family of graphs are formed in the order of n=p+q+s-l, which are obtained by identifying one pendant vertex of Ps with any vertex of Cp and the other pendant vertex of Ps with the center of K1,q. First, when s=2, there existed an L-cospectral mate graph. Next, by using the properties of Laplacian spectrum of a bipartite graph and adjacency spectrum of its line graph, it was proven that for s≥3 and when p is an even, the graph Hn(Cp,Ps,K1, q) should be determined by its Laplacian spectrum.%针对图的谱确定问题,在图Cp,Ps,K1,q的基础上定义了一类新图,符号表示为Hn(Cp,Ps,K1,q),它是通过重合Ps的一个悬挂点与Cp的任意一个点、另一个悬挂点与K1,q的中心点得到的顶点数为n=p+q+s-1的图.首先,找到并证明了当s=2时此类图存在一对L-同谱图.然后,利用二分图的Laplacian谱与其对应线图的邻接谱的性质,证明了当s≥3且p为偶数时,图Hn(Cp,Ps,K1,q)由Laplacian谱确定.