图簇Y_(λ_kδ)∪β_kS_δ~*的伴随分解及其补图的色等价性

The Factorization of Adjoint Polynomials of Graphs Y_(λ_kδ)^(S^*)∪β_kS_δ~* and Chromatically Equivalence Analysis

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.

Let Pn be the path with n vertices and let S＊δ（δ=rn＋1） be the graph consisting of rPn＋1 by coinciding one vertex of degree 1 of each component of rPn＋1. We denote by Yλ1δS＊ the graph consisting of r1S＊δ and S＊δ by adjacenting the vertex of degree r of every component of r1S＊δ with the vertex of degree r of S＊δ, respectively, and let Yλ2δ S＊ be the graph obtained from Yλ2δ S＊ and δ S＊ by adjacenting the vertex of degree r＋r1 of every component of r2 Yλ1δ S＊ with the vertex of degree r of S δ ＊, respectively, In geaeral, Yλκδ S＊ be the graph consisting of by adjacenting the vertex of degree of every component of with the vertex of degree r of , By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs Furthermore, We obtain structure characteristics of chromatically equivalent graphs of their complements.