On chromatic polynomials of regular graphs and modified wheels - Aves, Lovelina A. (Animo Repository, 1994)
Let P(G,y) denote the chromatic polynomial of a graph G expressed in the variable y. A graph G is chromatically unique if P(G,y) = P(H,y) implies that H is isomorphic to G. It is proven that complements of partial matching forest are chromatically unique. An infinite family of counterexamples to the conjecture that all regular graphs are chromatically unique is constructed. It is shown that the coefficients of chromatic polynomials of certain connected graphs, relative to the three basis, do not exhibit the strong logarithmic concavity property. Many of the coefficients have equal absolute values.