chromically equivalent graphs

Two nonisomorphic graphs are said to be chromatically equivalent (also termed "chromically equivalent by Bari 1974) if they have identical chromatic polynomials. A graph that does not share a chromatic polynomial with any other nonisomorphic graph is said to be a chromatically unique graph. The chromatically equivalent simple graphs on five or fewer vertices are illustrated above. Bari gives a number of chromatically equivalent graph pairs on 11 to 17 vertices that are planar triangulations. It appears to be the case that all resistance-equivalent graphs are also chromatically equivalent.

chromatically unique graph | chromatic polynomial | resistance-equivalent graphs