若干图运算的特征多项式计算  

The Characteristic Polynomials of Some Graph Operations

作　　者：邢抱花 孙旻昊 XING Baohua;SUN Minhao(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《安庆师范大学学报（自然科学版）》2023年第3期38-43,共6页Journal of Anqing Normal University(Natural Science Edition)

基　　金：安徽省高校自然科学研究重点项目(KJ2021A0650);省级研究生线下示范课程(2022xxsfkc038)。

摘　　要：设G是一个简单的无向图,RT (G)是将G的每条边和每一个顶点变换为C3(3阶的圈)所得到的图,而RK (G)是将G的每条边变换为C3(3阶的圈)且每一个顶点变换为Ck(k≥4阶的圈)所得到的图。本文给出了当G为半正则二部图时RT (G)的特征多项式,以及当G为正则图时RK (G)的特征多项式,并以此提出了构造邻接矩阵同谱图的图运算方法。Let G be a simple and undirected graph,and RT(G)be the graph obtained by turning each edge and vertex of G into C3(the cycle of order 3).RK(G) be the graph obtained by turning each edge of G into C3 and each vertex of G into Ck(the cycle of order k,k≥4).In this paper,we deduce the explicit expression of characteristic polynomials of RT(G)of a semi-regular bipartite graph G and RK(G) of a k-regular graph G.As an application,we propose graph operation approach to construct the adjacency co-spectral graphs.

关 键 词：特征多项式 邻接矩阵 半正则二部图 正则图 

分 类 号：O157.5[理学—数学]