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TETRAVALENT ARC-TRANSITIVE GRAPHS WITH UNBOUNDED VERTEX-STABILIZERS

Part of: Permutation groups

Published online by Cambridge University Press:  15 March 2011

PRIMOŽ POTOČNIK ,
PABLO SPIGA  and
GABRIEL VERRET
PRIMOŽ POTOČNIK
Affiliation:
Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia (email: primoz.potocnik@fmf.uni-lj.si)
PABLO SPIGA*
Affiliation:
School of Mathematics and Statistics, The University of Western Australia, Crawley, WA 6009, Australia (email: spiga@maths.uwa.edu.au)
GABRIEL VERRET
Affiliation:
Institute of Mathematics, Physics, and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia (email: gabriel.verret@fmf.uni-lj.si)
*
✉For correspondence; e-mail: spiga@maths.uwa.edu.au
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Abstract

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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.

Keywords

valency fourarc-transitive

MSC classification

Secondary: 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 1 , August 2011 , pp. 79 - 89
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The second author is supported by UWA as part of the Australian Council Federation Fellowship Project FF0776186.

References

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