On Chromatic Uniqueness of Some Complete Tripartite Graphs

Abstract

Let P(G,x) be a chromatic polynomial of a graph G. Two graphs G and H are called chromatically equivalent iff P(G,x)=H(G,x). A graph G is called chromatically unique if G≃H for every H chromatically equivalent to G. In this paper, the chromatic uniqueness of complete tripartite graphs K(n1,n2,n3) is proved for n1⩾n2⩾n3⩾2 and n1−n3⩽5.