Chromatic classes of 2-connected (n,n+4)-graphs with at least four triangles Original Research Article

For a graph G, let P(G) be its chromatic polynomial. Two graphs G and H are chromatically equivalent, written G∼H, if P(G)=P(H). A graph G is chromatically unique if P(H)=P(G) implies that H≅G. In this paper, we determine all equivalence classes of 2-connected (n,n+4)-graphs with at least four triangles under the equivalence relation ‘∼’. As a by product of these, we obtain various new families of chromatically equivalent graphs and chromatically unique graphs.