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 \(G\simeq H\) for every \(H\) chromatically equivalent to \(G\). In this paper, the chromatic uniqueness of complete tripartite graphs \(K(n_1, n_2, n_3)\) is proved for \(n_1 \geqslant n_2 \geqslant n_3 \geqslant 2\) and \(n_1 - n_3 \leqslant 5\).