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Additional Abstracts<br />
Friday 4:35–5:00 109 Oelman Hall<br />
2-arc transitive polygonal graphs <strong>of</strong> high girth<br />
Ákos Seress<br />
The Ohio State <strong>University</strong><br />
Abstract<br />
A near-polygonal graph is a graph Γ with a distinguished set C <strong>of</strong> cycles <strong>of</strong> common length m such<br />
that each path <strong>of</strong> length two lies in a unique element <strong>of</strong> C. If m is the girth <strong>of</strong> Γ then the graph is<br />
called polygonal.<br />
Polygonal graphs are Manley Perkel’s invention. In his thesis, he introduced two infinite families<br />
<strong>of</strong> 2-arc transitive, near-polygonal graphs <strong>of</strong> valency 5 and 6, which are orbital graphs <strong>of</strong> special linear<br />
groups. In this talk, we report on computer searches for polygonal graphs in Perkel’s families. The<br />
largest examples we have found have girth 23 and the number <strong>of</strong> vertices is over 10 17 .<br />
18
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