Chromatic Equivalence Classes of Certain Generalized Polygon Trees, \(II\)

Abstract

Let \(P(G)\) denote the chromatic polynomial of a graph \(G\). Two graphs \(G\) and \(H\) are chromatically equivalent, written \(G \sim H\), if \(P(G) = P(H)\). A graph \(G\) is chromatically unique if for any graph \(H\), \(G \sim H\) implies that \(G\) is isomorphic with \(H\). In “Chromatic Equivalence Classes of Certain Generalized Polygon Trees”, Discrete Mathematics Vol. \(172, 108–114 (1997)\), Peng \(et\; al\). studied the chromaticity of certain generalized polygon trees. In this paper, we present a chromaticity characterization of another big family of such graphs.