Starter sequences are natural generalizations of well-known Skolem sequences. In this paper, we introduce different types of starter sequences and determine some of the conditions for their existence; we also extend the results to [Formula: see text]-fold starter sequences and excess starter sequences.
A graph on 2 vertices can be starter-labelled, if the vertices can be given labels from the nonzero elements of the additive group Z 2 +1 such that each label , either or −1 , is assigned to exactly two vertices and the two vertices are separated by either edges or −1 edges, respectively. Mendelsohn and Shalaby have introduced Skolem-labelled graphs and determined the conditions ofwindmills 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.
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