Chromatic uniqueness of certain tripartite graphs identified with a path / G.C. Lau and Y.H. Peng

For a graph G, let P (G) be its chromatic polynomial. Two graphs G and H are chromatically equivalent if P(G) = P(H). A graph G is chromatically unique if P(H) = P(G) implies that H == G. In this paper, we classify the chromatic classes of graphs obtained from K2,2,2 u Pm (m ≥ 3) (respectively, (K2,2,2 - e) u Pm (m ≥ 5) where e is an edge of K2,2,2) by identifying the end vertices of the path Pm with any two vertices of K2,2,2 (respectively, K2,2,2 - e). As a by-product of this; we obtained some families of chromatically unique and chromatically equivalent classes of graphs.