关于图Cn1,n2,n3,n4及Cp,q,s的邻接谱

图的谱确定问题是图论中的一个重要问题,它是根据已知的特征值去确定图形,一般说来这是一件很困难的事.图论界的许多学者研究了一些特殊情形,主要涉及图的邻接谱(或图的Laplacian谱)的研究,其研究的一般途径是通过图的邻接矩阵(或Laplacian矩阵)表示,建立图的拓扑结构(特别是图的各种不变量).通过矩阵论,以及组合矩阵论中的经典结论,用于图的拓扑结构的研究.在已有文献的基础上研究了Cn1,n2,n3,n4图和Cp,q,s图的邻接谱问题,得到了不同构的Cn1,n2,n3,n4图及Cp,q,s图没有相同的邻接谱这个结论.

On the Adjacency Spectrum of Cn1,n2,n3,n4 andCp,q,s Graphs

Determination of the spectrum of a graph is an important issue in graph theory.It is a difficult task to determine a graph according to its characteristic values.Many scholars in the field of graph theory studied some special cases in which the adjacent spectrum(or Laplacan spectrum) of graphs is involved.The main study approach is that by using the adjacent matrix(or Laplacian matrix),the topolgical structure is established and different invariants are abtained.In this paper,by using some classical conclusions in combinatorial matrix theory,the topological structure and the adjacent spectrum of Cn1,n2,n3,n4 graph and Cp,q,s graph are investigated.It is proved that,for nonisomorphic graphs of these two types,there is no same adjacent spectrum.