Starter Labelling of k-Windmill Graphs with Small Defects

A graph on vertices can be starter-labelled, if the vertices can be given labels from the nonzero elements of the additive group such that each label , either or , is assigned to exactly two vertices and the two vertices are separated by either edges or edges, respectively. Mendelsohn and Shalaby have introduced Skolem-labelled graphs and determined the conditions of -windmills to be Skolem-labelled. In this paper, we introduce starter-labelled graphs and obtain necessary and sufficient conditions for starter and minimum hooked starter labelling of all -windmills.