Technical report: the chromatic uniqueness of a family of 6-bridge graphs θ(3,3,3,3,b,c) / Wan Noor Ain Wan Ahmad Saidi, Nurul Syafika Muhammad and Fakhira Juhari

A chromatic polynomial is denoted as P(G, λ ) while for graph H is P(G, λ ). Both graph of G and H are equivalently chromatic can be written in the form of P( G, λ ) = P(H, λ ). The chromatically unique of H, G ~ H that implies the graph G is an isomorphic to graph H. The multigraph are also known as a multi edges graph. Two different vertices which connected with every edge will also connected with other edges. The multigraph with two vertices and k edges is denotes as θk. In addition, a multi-bridge graph or a k- bridge graph are also known as the subdivision of θk. In this study we continue to solve a new problem of chromaticity of 6-bridge graph, that is θ(3,3,3,3,b,c) and prove the chromatic uniqueness of a new family of 6-bridge graphs.