Abstract.
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 G. We denote by F(G) the set of all complete graphs onto which G can be folded. We show here that if p and q are the largest and smallest orders, respectively, of the complete graph in F(W n ) or F(F n ), then K s is in F(W n ) or F(F n ) for each s, q≤s≤p. Lastly, we shall also determine the exact values of p and q.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: October, 2001 Final version received: June 26, 2002
Rights and permissions
About this article
Cite this article
Gervacio, S., Guerrero, R. & Rara, H. Folding Wheels and Fans. Graphs Comb 18, 731–737 (2002). https://doi.org/10.1007/s003730200058
Issue Date:
DOI: https://doi.org/10.1007/s003730200058