Geodesic
A construction of an infinite family of 2-arc transitive polygonal graphs of arbitrary even girth
Journal of Algebraic Combinatorics, Tome 33 (2011) no. 1, pp. 95-109.

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Summary: A near-polygonal graph is a graph $\Gamma $ which has a set $C$ mathcalC of $m$-cycles for some positive integer $m$ such that each 2-path of $\Gamma $ is contained in exactly one cycle in $C$ mathcalC. If $m$ is the girth of $\Gamma $, then the graph is called polygonal. We provide a construction of an infinite family of polygonal graphs of arbitrary even girth with 2-arc transitive automorphism groups, showing that there are infinitely many 2-arc transitive polygonal graphs of every girth.
Keywords: keywords algebraic graph theory, polygonal graph, 2-arc transitive graph 
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     title = {A construction of an infinite family of 2-arc transitive polygonal graphs of arbitrary even girth},
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Swartz, Eric. A construction of an infinite family of 2-arc transitive polygonal graphs of arbitrary even girth. Journal of Algebraic Combinatorics, Tome 33 (2011) no. 1, pp. 95-109. http://geodesic.mathdoc.fr/item/JAC_2011__33_1_a4/