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Tetravalent arc-transitive graphs with unbounded vertex-stabilizers. (English) Zbl 1222.05102

Summary: 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.

MSC:

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
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[1] DOI: 10.1007/978-1-4612-0731-3 · doi:10.1007/978-1-4612-0731-3
[2] Praeger, European J. Combin. 10 pp 91– (1989)
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