点圈并图的匹配等价图类  

The Matching Equivalent Graphs Classes of Union Graph of Vertices and Cycles

作　　者：李丹阳 马海成[1] LI Dan-yang;MA Hai-cheng(Department of Mathematics,Qinghai Nationalities University,Xining 810007,China)

机构地区：[1]青海民族大学数学与统计学院,青海西宁810007

出　　处：《数学的实践与认识》2021年第24期153-159,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11561056,11661066);青海省自然科学基金(2016-ZJ-914);青海民族大学研究生创新项目(07M2021003)。

摘　　要：若两个图的匹配多项式相等,称这两个图匹配等价.设G是一个图,以[G]表示图G的所有匹配等价图构成的集合,称为图G的匹配等价图类.目的是刻画点圈并图的匹配等价图类,从多个点并一个圈,和一个点并多个圈两个维度研究了这个问题.比较两个图的匹配多项式最大根的信息,我们完全刻画了图nK_(1)∪C_(m)和K_(1)∪(∪_(i)∈AC_(i)),(6■A)以及它们的补图的匹配等价图类.If the matching polynomials of two graphs are equal,they are called matching equivalence.Let G be a graph,the set composed of all matching equivalent graphs of graph G is represented by[G],which is called the matching equivalent graph class of graph G.The purpose of this paper is to characterize the matching equivalent classes of union graphs of vertices and cycles.This problem is studied from two dimensions:union graphs of multiple vertices and a circle,and union graphs of vertex and multiple cycles.By comparing the information of the maximum root of matching polynomials of two graphs,we completely characterize the matching equivalence classes of graphs nK_(1)∪C_(m),K_(1)∪(∪_(i)∈AC_(i)),(6■A)and their complement graphs.

关 键 词：匹配多项式 匹配等价 匹配唯一 

分 类 号：O157.5[理学—数学]