Chromaticity of certain tripartite graphs identified with a path

For a graph G  , let P(G)P(G) be its chromatic polynomial. Two graphs G and H   are chromatically equivalent if P(G)=P(H)P(G)=P(H). A graph G   is chromatically unique if P(H)=P(G)P(H)=P(G) implies that H≅GH≅G. In this paper, we classify the chromatic classes of graphs obtained from K2,2,2∪Pm(m⩾3)K2,2,2∪Pm(m⩾3), (K2,2,2-e)∪Pm(m⩾5)(K2,2,2-e)∪Pm(m⩾5) and (K2,2,2-2e)∪Pm(m⩾6)(K2,2,2-2e)∪Pm(m⩾6) by identifying the end-vertices of the path PmPm with any two vertices of K2,2,2K2,2,2, K2,2,2-eK2,2,2-e and K2,2,2-2eK2,2,2-2e, respectively, where e   and 2e2e are, respectively, an edge and any two edges of K2,2,2K2,2,2. As a by-product of this, we obtain some families of chromatically unique and chromatically equivalent classes of graphs.