A note on "Folding wheels and fans."

In S.Gervacio, R.Guerrero and H.Rara, Folding wheels and fans, Graphs and Combinatorics 18 (2002) 731-737, the authors obtain formulas for the clique numbers onto which wheels and fans fold. We present an interpolation theorem which generalizes their theorems 4.2 and 5.2. We show that their formula for wheels is wrong. We show that for threshold graphs, the achromatic number and folding number coincides with the chromatic number

Folding wheels and fans

If two non-adjacent vertices of a connected graph that have a common neighbor are identified and the resulting multiple edges are reduced to simple edges, then we obtain another graph of order one less than that of the original graph. This process can be repeated until the resulting graph is complete. We say that we have folded the graph onto complete graph. This process of folding a connected graph G onto a complete graph induces in a very natural way a partition of the vertex-set of C. We denote by F(G) the set of all complete graphs onto which C can be folded. We show here that if p and q are the largest and smallest orders, respectively, of the complete graph in F(Wn) or F(Fn), then Ks, is in F(Wn) or F(Fn) for each s, q ≤ s ≤ p. Lastly, we shall also determine the exact values of p and q