一类边替换图的平均拉普拉斯多项式  

Average Laplacian polynomials of a family of edge-replaced graphs

作　　者：阙林凤 陈海燕[1] QUE Linfeng;CHEN Haiyan(School of Sciences,Jimei University,Xiamen 361021,China)

机构地区：[1]集美大学理学院,福建厦门361021

出　　处：《厦门大学学报（自然科学版）》2022年第2期163-166,共4页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(11771181,12071180)。

摘　　要：设G和T是两个简单图,i和j是T中两个固定顶点,满足T-i和T-j同构.把G的每条边e=(u,v)替换成T,使得i=u,j=v,所得到的图称为边替换图,记为G[T].本文考虑了当G是一个d-正则图时,G[T]的平均拉普拉斯多项式和图G的平均拉普拉斯多项式之间的关系.并把所得结果具体应用到剖分图S(G)和三角扩展图R(G)这两类常见的变换图中,得到它们的平均拉普拉斯多项式和原图的平均拉普拉斯多项式之间的具体关系式.Let G and T be two simple graphs.i and j are two fixed vertices in T such that T-i and T-j are isomorphic.The edge-replaced graph G[T]is the graph obtained from G by replacing each edge e=(u,v)of G with T such that i=u,j=v.In this paper,we consider the relations between the average Laplacian polynomial of G[T]and that of G,when G is an regular graph.As applications,for the subdivision graph S(G)and triangular extension graph R(G),we obtain the explicit relations between their average Laplacian polynomials and that of the original graph.

关 键 词：边替换图 平均拉普拉斯多项式 剖分图 三角扩展图 

分 类 号：O157.5[理学—数学]