A note on chromatic uniqueness of graphs

Abstract

Abstract We proved that if a connected graph is chromatically unique, then it has at most two blocks. Furthermore each of these blocks is vertex‐transitive and chromatically unique. It is then shown that if the two blocks of a connected graph G are H and K 2 , then G is chromatically unique if and only if H is vertex‐transitive and chromatically unique. This answers a conjecture of Whitehead and Zhao in the affirmative.