CHROMATIC CLASSES OF CERTAIN 2-CONNECTED (N, N+ 2)-GRAPHS

Let P(G) denote the chromatic polynomial of a graph G. Two graphs G and H are chromatically equivalent, written G approximately H, if P(G) = P(H). A graph G is chromatically unique if G congruent-to H for any graph H such that H approximately G. Let G denote the class of 2-connected graphs of order n and size n + 2 which contain a 4-cycle or two triangles. It follows that if G is-an-element-of G and H approximately G, then H is-an-element-of G. In this paper, we determine all equivalence classes in G under the equivalence relation 'approximately' and characterize the structures of the graphs in each class. As a by-product of these, we obtain three new families of chromatically unique graphs.