图的伴随多项式的两个因式分解定理及其应用

Two Factorization Theorems of Adjoint Polynomials of Graphs with Application

中文关键词:  色多项式  伴随多顶式  因式分解  色等价性  色唯一性

英文关键词:chromatic polynomial  adjoint polynomial  factorization  chromatically equivalence  chromatically uniqueness

中文摘要:

      设G是m阶连通图,P_m是m个顶点的路.令S_km+1^G(i)表示把kG的每一个分支的第i(1≤i≤m)个顶点依次与星图S_k+1的k个1度顶点重迭后得到的图;令G_i1^S*(q,km)表示q阶图G的顶点V_i1与S_km+1^p(1)的k度顶点重迭后得到的图

英文摘要:

      Let G be a connected graph of order p and P_m be a path with m vertices. Let S_km+1^G(i) denote the graph consisting of rG and the star S_k+1 by coinciding the ith vertex of everyone of rG with k-1 vertices of degree 1 of S_k+1; let G_i1^S*(q,km) denote the graph obtained from a graph G of order 1 and S_km+1^p(1) by coinciding the vertex v_il of G with the vertex of degree k of S_km+1^p(1). We give and prove that factorization theory of adjoint polynomials of graphs S_km+1^G(i)∪(k-1)K₁ and G_i1^S*(q,km),and we obtain some structure characteristics of the chromatically equivalent graphs of their complements.