A complete solution to the chromatic equivalence class of graph ζ_n~1

摘要

Two graphs are defined to be adjointly equivalent if their complements are chromatically equivalent. By h(G, x) and P(G, λ) we denote the adjoint polynomial and the chromatic polynomial of graph G, respectively. A new invariant of graph G, which is the fifth character Rs(G), is given in this paper. Using this invariant and the properties of the adjoint polynomials, we firstly and completely determine the adjoint equivalence class of the graph ζ_n~1.According to the relations between h(G, x) and P(G, λ), we also simultaneously determine the chromatic equivalence class of ζ_n~1.