Classes of chromatically equivalent graphs and polygon trees

AbstractWe give the definition of complete classes of chromatically equivalent graphs and some results on this topic. We give an invariant for generalized polygon tree under chromatic equivalence, which is useful in searching for chromatically equivalent graphs. As a consequence we show that {{Cio,…,Ci,k},k{K>2}} is a complete class of a chromatically equivalent graphs, which solves a problem raised in Whitehead Jr (1988)