Tetravalent arc-transitive graphs with unbounded vertex-stabilisers

Details Tetravalent arc-transitive graphs with unbounded vertex-stabilisers Tetravalent arc-transitive graphs with unbounded vertex-stabilisers

2010-10-13

arxiv.org/abs/1010.2549v1

Mathematics

Combinatorics

9 pages

Scientific paper

It has long been known that there exist finite connected tetravalent arc-transitive graphs with arbitrarily large vertex-stabilisers. 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-stabilisers, each significant for its own reason.

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