完全多部图的拉普拉斯特征多项式

摘要

The existence problem of Laplacian integral graphs is studied. Let A(G) denotes the adjacency matrix of graph G with n vertices and D(G) denotes the degree diagonal matrix of graph C. The Laplacian matrix of graph G is L(G) =D( G)-A(G). By studying the Laplacian characteristic polynomial of the complete multipartite graph Kp1,P1... ,pr , it is obtained that all the complete multipartite graphs Kp1,p2,…,pr are Laplacian integral.%研究拉普拉斯整图的存在性问题.用A(G)表示有n个顶点的简单图G的邻接矩阵,D(G)表示图G的顶点度对角矩阵.图G的拉普拉斯矩阵为L(G)=D(G)-A(G).通过研究完全多部图Kp1,p2,…,pr的拉普拉斯特征多项式,得到了所有的完全多部图Kp1,p2.…pr都是拉普拉斯整图.