Chromatically Unique Multibridge Graphs - Dong, F. M.; Teo, K. L.; Little, C. H. C.; Hendy, M.; Koh, K. M. (The Electronic Journal of Combinatorics, 2004)
Let θ(a_1,a_2,…,a_k) denote the graph obtained by connecting two distinct vertices with k independent paths of lengths a_1,a_2, …,a_k respectively. Assume that 2a_1a_2… a_k. We prove that the graph θ(a_1,a_2, …,a_k) is chromatically unique if a_k < a_1+a_2, and find examples showing that θ(a_1,a_2, …,a_k) may not be chromatically unique if a_k=a_1+a_2.