On the chromatic uniqueness of the graph W(n, n-2) + Kk

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