# Folding wheels and fans

## College

College of Science

## Department/Unit

Mathematics and Statistics Department

## Document Type

Conference Proceeding

## Source Title

Graphs and Combinatorics

18

4

731

737

12-1-2002

## 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 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.

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## Digitial Object Identifier (DOI)

10.1007/s003730200058

Mathematics