A new family of chromatically unique 6-bridge graph

Abstract

For a graph G, let P (G, λ) denote the chromatic polynomial of G. Two graphs G and H are chromatically equivalent (or simply χ -equivalent), denoted by G ~ H, if P (G, λ) = P (H, λ). A graph G is chromatically unique (or simply λ-unique) if for any graph H such as H ~ G, we have H ≅ G, i.e, H is isomorphic to G. In this paper, the chromatic uniqueness of a new family of 6-bridge graph θ(a, a, b, b, b, c) where 2 ≤ a ≤ b ≤ c, is investigated.