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. © Australian Mathematical Publishing Association Inc. 2011.
Potočnik, P., Spiga, P., & Verret, G. (2011). Tetravalent arc-transitive graphs with unbounded vertex-stabilizers. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 84(1), 79-89 [10.1017/S0004972710002078].
Tetravalent arc-transitive graphs with unbounded vertex-stabilizers
SPIGA, PABLO
;
2011
Abstract
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. © Australian Mathematical Publishing Association Inc. 2011.
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