Technical report: chromaticity of 6-bridge graph θ(3,3,3,b,c,c) / Madihah Azmi, Emy Norfariha Mustapha and Asmaa' Amalina Harun

Consider two graph G and H. For graph G, let P(G,λ) denote the chromatic polynomial of a graph G and P(H,λ) denote the chromatic polynomial of a graph H. Graph G and H are chromatically equivalent, G ~ H, if P(G,λ) = P(H,λ). A graph G is said to be chromatically unique, x-unique, if for any graph H, H is isomorphic to G, denoted by G ~ H implies G ≅ H. To find the uniqueness of the graph, we will use the theorems and lemmas that have been used by others researchers in finding the k-bridge graph for k ≤ 5. In this project, we have studied about the chromatic uniqueness of a new family of 6-bridge graph which is θ(3,3,3,b,c,c).