Fold thickness of graphs

The graph G' obtained from a graph G by identifying two nonadjacent vertices in G having at least one common neighbor and reducing the resulting multiple edges to simple edges is called a 1-fold of G. A uniform k-folding of a graph G is a sequence of graphs G = G(0), G(1), G(2), ..., G(k), where G(i)(+1)( )is a 1-fold of G(i) for i = 0, 1, 2, ..., k - 1 such that all graphs in the sequence are singular or all of them are nonsingular. The largest k for which there exists a uniform k-folding of G is called fold thickness of G and this concept was first introduced in [1]. In this paper, we determine fold thickness of lollipop graph, web graph, helm graph and rooted product of complete graphs and paths.