Chromatic uniqueness in a family of 2-connected graphs Original Research Article

In this note, it is shown that all graphs Fn,k for odd integer n ⩾ 5, and integer k ⩾ 1 are χ-unique. This is a partial solution of one of the problems stated in [2] (see Problem 5 [2]). Fn,k is a graph which is a K2-gluing of K1 + Pn−1 and k paths on three vertices P3, where K2 is the graph induced by two vertices of minimum degree in each of these graphs. An open problem is stated.