几类图的伴随多项式的分解及其色等价性分析  

The factorizations of adjoint polynomials of kinds of graphs and chromatically equivalence analysis

作　　者：熊鹏飞 

机构地区：[1]青海交通职业技术学院,青海西宁810016

出　　处：《青海师范大学学报（自然科学版）》2017年第3期11-14,41,共5页Journal of Qinghai Normal University(Natural Science Edition)

摘　　要：设Ρn和Cn分别表示具有n个顶点的路和圈,令Ψ2(,n)表示把路Ρn的一个1度点与Ρ3一个2度点重迭后得到的图,令φrm+1表示把(r-1)Cm+1的每个分支的一个2度点与Ρm+1的一个1度点重迭后得到的图,令δ=rm+1,ρφnδ表示由Ρn与φrm+1组合而成的图.我们运用图的伴随多项式的性质,讨论了图ρφnδ的伴随多项式,给出并证明了这些图簇的伴随多项式的因式分解式,进而证明了这些图类的补图的色等价性,得到了这些图的色等价图的结构特征.We use the symbol Pn to denote a path with n vertices and Cn to denote a cycle with n verti- ces,and x/t（2,n） be the graph obtaining from Pnand P3 by coinciding a vertex of degree 1 of-Pn with a ver- tex of degree 2 of P3, We denote by φm＋1 the graph consisting of （r-1）Cm＋l and Pm＋1 by coinciding a ver- tex of degree 2 of every component of （r--1）Cm＋l with a vertex of degree 1 of Pm＋1 in turn, Let δ=rm＋ 1, We use the symbol ρns to denote the combinatorial graphs by Pn and φrm＋1. By applying the properties of adjoint polynomials, we discuss the factorizations of adjoint polynomials of these graphs, Furthermore, We prove that chromatically equivalence of complements of these graphs, We obtain structure characteris- tics of chromatically equivalent graphs of their complements.

关 键 词：色多项式 伴随多项式 因式分解 色等价性 

分 类 号：O175[理学—数学]