The Chromatic Equivalence Class of Graph \(\psi_n^3({n-3,1})\)

Abstract

Two graphs are defined to be adjointly equivalent if their complements are chromatically equivalent. Recently, we introduced a new invariant of a graph \(G\), denoted as \(R_5(G)\). Using this invariant and the properties of the adjoint polynomials, we completely determine the adjoint equivalence class of \(\psi_n^3({n-3,1})\). According to the relations between adjoint polynomial and chromatic polynomial, we also simultaneously determine the chromatic equivalence class of \(\psi_n^3({n-3,1})\).