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Some conditions for 1-transitivity

By Mark E. Watkins

Abstract

AbstractEvery 1-transitive finite or infinite graph is clearly both vertex-transitive and edge-transitive. The converse being false, this paper considers various sufficient conditions for a vertex-transitive, edge-transitive graph to be 1-transitive. Following a survey of known results, a new sufficient condition is presented for infinite, 3-connected, planar graphs, and a conjecture is proposed for infinite planar graphs of connectivity 2. Finally, a new infinite family of infinite graphs is constructed that are vertex-transitive and edge-transitive but not 1-transitive

Publisher: Published by Elsevier B.V.
Year: 1992
DOI identifier: 10.1016/0012-365X(92)90299-U
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