A Family of Chromatically Unique \(5\)-Bridge Graphs

Abstract

Let \(P(G; \lambda)\) denote the chromatic polynomial of a graph \(G\), expressed in the variable \(\lambda\). Then \(G\) is said to be chromatically unique if \(G\) is isomorphic with \(H\) for any graph \(H\) such that \(P(H; \lambda) = P(G; \lambda)\). The graph consisting of \(s\) edge-disjoint paths joining two vertices is called an \(s\)-bridge graph. In this paper, we provide a new family of chromatically unique \(5\)-bridge graphs.