中文摘要：

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.

英文摘要：

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-1,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.