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图簇Y_(λ_kδ)∪β_kS_δ~*的伴随分解及其补图的色等价性
引用本文:郝萃菊,张秉儒.图簇Y_(λ_kδ)∪β_kS_δ~*的伴随分解及其补图的色等价性[J].数学的实践与认识,2012(22):251-264.
作者姓名:郝萃菊  张秉儒
作者单位:青海大学财经学院;青海师范大学数学系
基金项目:国家自然科学基金(10671008)
摘    要:设P_n是具有n个顶点的路,令δ=rn+1,我们S_δ~*表示把rP_(n+1)的每个分支的一个1度点重迭在一起得到的图.用Y_(λ_1δ)~(S*)表示把r_1S_δ~*中每个分支的r度顶点与S_δ~*的r度顶点依次邻接后得到的图,Y_(λ_2δ)~(S*)表示把用r_2Y_(λ_1δ)~(S*)中每个分支的r+r1度顶点与S_δ~*的r度顶点依次邻接后得到的图,一般地,Y_(λ_kδ)~(S*)表示把用r_kY_(λ_(k-1)δ)~(S*)中每个分支的r+r_k-1度顶点与S_δ~*的r度顶点依次邻接后得到的图,运用图的伴随多项式的性质,证明了图Y_(λ_kδ)~(S*)∪β_kS_δ~*的伴随多项式的因式分解定理,进而得到了这类图的补图的色等价性.

关 键 词:色多项式  伴随多项式  因式分解  色等价性

The Factorization of Adjoint Polynomials of Graphs Y_(λ_kδ)~(S~*)∪β_kS_δ~* and Chromatically Equivalence Analysis
HAO Cui-ju,ZHANG Bing-ru.The Factorization of Adjoint Polynomials of Graphs Y_(λ_kδ)~(S~*)∪β_kS_δ~* and Chromatically Equivalence Analysis[J].Mathematics in Practice and Theory,2012(22):251-264.
Authors:HAO Cui-ju  ZHANG Bing-ru
Institution:1.Finance and Economics College,Xingni 810006,China) (2.Department of Mathematics,Qinghai Normal University,Xining 810008,China)
Abstract:Let P_n be the path with n vertices and let S_∞~*(5 = rn + 1) be the graph consistingof rP_(n+1) by coinciding one vertex of degree 1 of each component of rP_(n+1).We denote by Y_(λ_1δ)~(S*)the graph consisting of r_1S_δ~* and S_δ~* by adjacenting the vertex of degree r of every componentof r_1 S_δ~* with the vertex of degree r of S_δ~*,respectively,and let Y_(λ_2δ)~(S*) be the graph obtained fromr_2Y_(λ_1δ)~(S*)and S_δ~* by adjacenting the vertex of degree r+r_1 of every component of r_2Y_(λ_1δ)~(S*) with thevertex of degree r of S_δ~*,respectively,In general,Y_(λ_kδ)~(S*) be the graph consisting ofτ_kY_(λ_(k-1))~(S*)andS_δ~* by adjacenting the vertex of degree r + r_(k-1) of every component of r_kY_(λ_(k-1)δ)~(S*) with thevertex of degree r of S_δ~*,By applying the properties of adjoint polynomials,We prove thatfactorization theorem of adjoint polynomials of kinds of graphs Y_(λ_kδ)~(S*)∪β_k S_δ~*,Furthermore,We obtain structure characteristics of chromatically equivalent graphs of their complements.
Keywords:chromatic polynomial  adjoint polynomials  factorization  chromatically equivalence
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