浙江大学学报（理学版）2024，Vol.51Issue(2)：172-177,6.DOI:10.3785/j.issn.1008-9497.2024.02.005
可交换图的一些注记
A note on commutative graphs
摘要
Abstract
Two simple graphs are commutative if there exists a labelling of their vertices such that their adjacency matrices can commute.This paper gives three necessary conditions ensuring the commutativity of certain graphs from Perron vectors,the number of main eigenvalues,the regularity of graphs.Then we construct new commutative graphs by graph Kronecker product,Cartesian product and circulant matrix.Finally,for two commutative graphs,we provide two algorithms that can express one adjacency matrix as the matrix polynomial of another adjacency matrix with distinct eigenvalues,and compare their merits.Commutative graphs sharing common eigenvectors are essential to the study of spectral graph theory.关键词
可交换图/正则图/循环图/克罗内克积/笛卡尔积Key words
commutative graph/regular graph/circulant graph/Kronecker product/Cartesian product分类
数理科学引用本文复制引用
吴寒,刘奋进,尚凡琦,周艳红,阮昊桐..可交换图的一些注记[J].浙江大学学报（理学版）,2024,51(2):172-177,6.基金项目
陕西省自然科学基础研究计划项目(2021JM-149) （2021JM-149）
长安大学2020年大学生创新创业训练计划项目(S202010710247). （S202010710247）
