三类符号变换图的特征多项式  

The characteristic polynomials of three classes of sign transform graphs

作　　者：张亚南 陈海燕[1] ZHANG Ya nan;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）》2020年第2期287-290,共4页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(11771181,11571139)。

摘　　要：令G=(V(G),E(G))是n个点、m条边的简单图,σ:E(G)→{+1,-1}是定义在边集E(G)上的符号映射,称Γ=(G,σ)为G的一个符号图.给定一个符号图Γ,Belardo和Simic定义了符号线图(Γ)和符号剖分图S(Γ),并得到它们邻接特征多项式和Γ的Laplacian特征多项式之间的关系.本文定义了另外三类符号变换图,即符号中间图、符号三角扩展图和符号全图,分别记为Q(Γ)、R(Γ)和T(Γ).当G是正则图,给出这三类符号变换图的邻接特征多项式和Laplacian特征多项式与原符号图对应多项式的关系.这些结果推广了一般图对应的已有结论.Let G=(V(G),E(G))be a simple graph of order n and size m,and letσ:E(G)→{+1,-1}be a mapping defined on the edges of G.We callΓ=(G,σ)a signed graph of G.Given a signed graphΓ,Belardo and Simicdefined the signed line graph(Γ)as well as the signed subdivision graph S(Γ)and obtained relations between their adjacency polynomials and Laplacian polynomials ofΓ.In this paper,we defined other three classes of signed transform graphs,signed middle graph,signed triangular extension graph and signed total graph,denoted by Q(Γ),R(Γ),T(Γ)respectively.When G is regular,we express the adjacency and Laplacian polynomials of the three classes of signed transform graphs in terms of those of original signed graphΓ.These results generalize the counterpart of unsigned graphs.

关 键 词：符号图 符号中间图 符号三角扩展图 符号全图 邻接特征多项式 Laplacian特征多项式 

分 类 号：O157.5[理学—数学]