Chromatic uniqueness of 6-bridge graph θ(3,3,b,c,c,c)

For a graph G, suppose P(G,l) be the chromatic polynomial of G. Two graphs G and H are said to be chromatically equivalent (or simply χ-equivalent), denoted by G ~ H, if P(G, λ)= P(H, λ). A graph G is said to be chromatically unique (or simply χ-unique) if for any graph H such that H ~ G, we have H ≅ G, i.e. H is isomorphic to G. In this paper, the chromatic uniqueness of a family of 6-bridge graphs, that is the graph of the form θ(3,3,b,c,c,c) is determined.