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A Family of Near-Polygonal Graphs of Valency 10 |
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| Authors: | ákos Seress Eric Swartz |
| Affiliation: | 1. Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH, 43210-1174, USA 2. Centre for the Mathematics of Symmetry and Computation, School of Mathematics and Statistics, University of Western Australia, Crawley, WA, 6009, Australia 3. Department of Mathematical Sciences, Binghamton University, Binghamton, NY, 13902-6000, USA |
| Abstract: | A near-polygonal graph is a graph ?? which has a set ${mathcal{C}}$ of m-cycles for some positive integer m such that each 2-path of ?? is contained in exactly one cycle in ${mathcal{C}}$ . If m is the girth of ?? then the graph is called polygonal. We provide a construction for an infinite family of 2-arc transitive near-polygonal graphs of valency 10 and provide a method for determining the length m of special cycles in graphs in this family. This provides us with some new instances of polygonal graphs as well. |
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