Graceful labellings of variable windmills using Skolem sequences

In this paper, we introduce graceful and near graceful labellings of several families of windmills. In particular, we use Skolem-type sequences to prove (near) graceful labellings exist for windmills with C3 and C4 vanes, and infinite families of 3, 5-windmills and 3, 6-windmills. Furthermore, we offer a new solution showing that the graph obtained from the union of t 5-cycles with one vertex in common (C 5) is graceful if and only if t ≡ 0, 3 (mod 4) and near graceful when t ≡ 1, 2 (mod 4).