The chromatic uniqueness of certain broken wheels

Abstract Let W ( n , k ) denote the graph of order n obtained from a wheel W n by deleting all but k consecutive spokes. It is known that W ( n ,1) ( n ⩾4) and W ( n ,2) ( n ⩾4) are χ-unique. Chao and Whitehead [1] showed that W ( n ,3) ( n ⩾5) and W ( n ,4) ( n ⩾6)are also χ-unique but pointed out that W (7,5) is not so. In this note, we prove that W ( n ,5) is χ-unique for n ⩾8.