完全图的剖分图的线图的谱

摘要

A graph G is called integral if all eigenvalues of the adjacency matrix A(a)of G are integers. Let L2(Kp)=L(S(Kp))be the line graph of the subdivision graph S(Kp) of the complete graph Kp. In this paper, we shall give the spectra and characteristic polynomials of S(Kp) and L2(Kp)from the theory on graphs. For the graph L2(Kp),we derive the characteristic polynomials for its complement graph, its line graph, the complement graph of its line graph and the line graph of its complement graph.We also prove these graphs are integral graphs.The discovery of these integral graphs is a new contribution to the research of integral graphs.%如果一个图G的邻接矩阵A(G)的特征多项式的所有特征值全为整数,则称图G是整的.设图L2(Kp):L(s(Kp))是完全图Kp的剖分图S(Kp)的线图.在这篇文章里,我们利用图的理论给出了S(Kp)和L2(Kp)的特征多项式及其谱.对于图L2(Kp),得到了其补图、线图、线图的补图及补图的线图的特征多项式.也证明了这些图都是整图.这些整图的发现是对整图的研究的一个新贡献.