The Factorization of Adjoint Polynomials of E^G（i）-class Graphs and Chromatically Equivalence Analysis

摘要

Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by ErGp(+i)(r-1) the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r-1 of Sr, while the i-th vertex of each component of (r-1)G be adjacented to r-1 vertices of degree 1 of Sr, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs ErGp(+i)(r-1) (r-1)K1 (1 ≤ i ≤ p). Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.