E~(G(i))类图簇的伴随多项式的因式分解及色性分析

设Sn+1是n+1个顶点的星图,G是任意的p阶连通图.ΨG(i)(n,p)表示把Sn+1的n度点与G的第i(1 i p)个顶点重迭后得到的图;ErG(p+i)(r-1)表示把rG的r-1个分支的第i个顶点依次与Sr的r-1个1度点邻接,同时把剩下的一个图G的第i个顶点与Sr的r-1度点重迭后得到的图.我们通过讨论图簇ErG(p+i)(r-1)∪(r-1)K1的伴随多项式的因式分解,证明了它的补图的色等价图的结构性质.

The Factorization of Adjoint Polynomials of EG(I) class Graphs and Chromatically Equivalence Analysis

Let S_(n+1) be the star with n+1 vertices,and let G be an arbitrary connected graph with p vertices.Denote by Ψ~(G(i))(n,p) the graph consisting of G and S_(n+1) by coinciding the ith vertex of G with the vertex of degree n of S_(n+1).and by E~(G(i))_(rp+(r-1)) the graph obtained from S_r and rG by coinciding the ith vertex of G with the vertex of degree r1 of S_r,while the ith vertex of each component of(r-1)G be adjacent to r-1 vertices of degree 1 of S_r,respectively.By studying the factorization formula of adjoint polynomials of the graphs E~(G(i))_(rp+(r-1))∪(r-1)K_1,we prove the structure proerties of chromatic equivalence of their complments.