On Skolem Labelling of Windmills

In a previous work “Skolem labelled graphs” \({[4]}\) we defined the Skolem labelling of graphs, here we prove that the necessary conditions are sufficient for a Skolem or minimum hooked Skolem labelling of all \(k\)-windmills. A \(k\)-windmill is a tree with \(k\) leaves each lying on an edge-disjoint path of length \(m\) to the centre. These paths are called the vanes.