Some families of chromatically unique bipartite graphs

Abstract

A graph is said to be chromatically unique (or χ-unique) if it is uniquely determined by its chromatic polynomial. Let K − r ( p, q) denote the family of graphs obtained from K p. q by deleting any r distinct edges. In this paper, we study the chromaticity of the graphs in K − r ( p, q). A sufficient condition is given for a member of K − r ( p, q) to be χ-unique and some families of χ-unique bipartite graphs are obtained.