Chromatically equivalent graphs are pairs of nonisomorphic graphs with identical chromatic polynomials. They are also called
chromically equivalent (Bari 1974) or cochromatic. 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 (1974) gives a number of chromatically equivalent graph pairs on 11 to 17 vertices that are planar triangulations.
Bari, R. A. "Chromatically Equivalent Graphs." In Graphs and Combinatorics (Ed. R. A. Bari and F. Harary).
Berlin: Springer-Verlag, pp. 186-200, 1974.Bari, R. A. "Recent
Results on Chromatically Equivalent Graphs." In Second International Conference
on Combinatorial Mathematics (New York, 1978).Ann. New York Acad. Sci.319,
37-46, 1979.
