Two families of chromatically unique graphs.

Let P(G) denote the chromatic polynomial of a graph G. A graph G is said to be chromatically unique if P(G) = P(H) implies that H is isomorphic to G. In this paper, We prove that a graph (resp., a bipartite graph) obtained from K2,4 U P3 (s ≥ 3) (resp., K3,3 U P3 (s ≥ 7)) by identifying the end vertices of the path Ps with any two vertices of the complete bipartite graph K2,4 (resp., K3,3) is chromatically unique.

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