resistance spectrum

Two nonisomorphic graphs that have equal resistance spectra (i.e., multisets of resistance distances) are said to be resistance-equivalent. All nonisomorphic simple graphs on eight or fewer vertices are determined by their resistance spectra. However, exactly 11 pairs of nonisomorphic graphs with nine vertices are resistance-equivalent, illustrated above (in the illustration, the numbers indicate the graph numbers in McKay's enumeration of 9-vertex graphs), where the second and third of these pairs were found by Baxter (1999b).

chromatically equivalent graphs | resistance distance