恰有两个主特征值的图与图的剖分

The Graphs with Exactly Two Main Eigenvalues and the Graph Partition

大量研究表明,图的主特征值的数量与图的结构有着密切关系.通过恰有两个主特征值的图的特征定义了2-邻域k-剖分图,研究了恰有两个主特征值的图与2-邻域k-剖分图之间的关系;同时给出一个2-邻域k-剖分图在k=2,3时为等部剖分的条件.

A great number of studies indicate that the number of main eigenvalues of a graph had affinities with the structure characteristic of graphs.It defines the 2-neighborκ-partition graph by the characteristic of graphs with exactly two main eigenvalues.This paper not only studies the relation of the 2-neighborκ-partition graph and the graph with exactly two main eigenvalues,but also gives conditions that the 2-neighborκ-partition graphs is converted to the equitable partition graphs forκ=2,3.