一些可交换图的刻画

Characterization of Some Commutative Graphs

两个图称为可交换的,如果存在一种顶点标号使得它们在该顶点标号下的邻接矩阵可交换。本文通过利用已知可交换图的性质及矩阵克罗内克积积运算、图联运算的性质,从已知可交换图出发构造出新的可交换图,对研究可交换图问题有重要促进作用。

Two graphs are called commuting if there exists a labelling of the vertices such that their adjacency matrix commute. In this paper, new commuting graphs are constructed from the known ones by using the properties of the commuting matrices, the Kronecker product operation of matrix and the joint operation of a graph, which promotes the study of commuting graphs.