2-arc Transitive Polygonal Graphs of Arbitrarily Large Girth and Degree
by
Eric Swartz
The Ohio State University

A near-polygonal graph is a graph G which has a set C of m-cycles for some positive integer m such that each 2-path of G is contained in exactly one cycle in C. If m is the girth of G then the graph is called polygonal. Up until now, the only examples of 2-arc transitive polygonal graphs with arbitrarily large degree had girth no larger than seven, and the 2-arc transitive polygonal graph with largest girth had degree five and girth twenty-three (in fact, even with no restrictions on the automorphism group, there were no examples of polygonal graphs with odd girth greater than twenty-three). In this talk, we provide construction of an infinite family of polygonal graphs of arbitrary girth m with 2-arc transitive automorphism groups, showing that there are 2-arc transitive polygonal graphs of arbitrarily large degree for each girth m ≥ 3.

Date received: March 30, 2009