σ-polynomials Original Research Article

Let G be a spanning subgraph of the complete bipartite graph Kn,n. In this paper, we obtain a formula relating Gc to Ḡc by a integral formula of the σ-polynomial of Gc (where Gc is the complement of G, and Ḡ is the complement of G in Kn,n). It shows that letting G,H be the spanning subgraphs of Kn,n, then Gc and Hc are chromatically equivalent if and only if Ḡc and H̄c are chromatically equivalent.