On the chromatic uniqueness of the graph W(n, n − 2) + Kk Original Research Article

Let W(n, m) denote the graph of order n obtained from the wheel Wn be deleting all but m consecutive spokes, and W(n, n − 2) + Kk, the join of W(n, n − 2) and Kk, which is obtained from the union of W(n, n − 2) and Kk by joining each vertex in Kk. In this paper, we prove that the graph W(n, n − 2) + Kk is chromatically unique for each integer n ⩾ 6 and integer k ⩾ 0.