chromically unique graph | determined by chromatic polynomial

Let P(G) denote the chromatic polynomial of a finite simple graph G. Then G is said to be chromatically unique if P(G) = P(H) implies that G and H are isomorphic graphs, in other words, if G is determined by its chromatic polynomial. If G and H are nonisomorphic but share the same chromatic polynomial, they are said to be chromatically equivalent. Cycle graphs are chromatically unique, as are Turán graphs. Named graphs that are chromatically nonunique include the 3- and 4-barbell graph, bislit cube, bull graph, claw graph, 3-matchstick graph, Moser spindle, 2-Sierpiński gasket graph, star graphs, triakis tetrahedral graph, and 6- and 8-wheel graphs.

bull graph | chromatic polynomial | determined by spectrum | isomorphic graphs