a1 Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia (email: firstname.lastname@example.org)
a2 School of Mathematics and Statistics, The University of Western Australia, Crawley, WA 6009, Australia (email: email@example.com)
a3 Institute of Mathematics, Physics, and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia (email: firstname.lastname@example.org)
It has long been known that there exist finite connected tetravalent arc-transitive graphs with arbitrarily large vertex-stabilizers. However, beside a well-known family of exceptional graphs, related to the lexicographic product of a cycle with an edgeless graph on two vertices, only a few such infinite families of graphs are known. In this paper, we present two more families of tetravalent arc-transitive graphs with large vertex-stabilizers, each significant for its own reason.
(Received October 13 2010)
(Online publication March 15 2011)
2010 Mathematics subject classification
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The second author is supported by UWA as part of the Australian Council Federation Fellowship Project FF0776186.