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 Kp.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.
