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Some conditions for 1-transitivity

✍ Scribed by Mark E. Watkins

Publisher: Elsevier Science
Year: 1992
Tongue: English
Weight: 665 KB
Volume: 109
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90299-u

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✦ Synopsis

Watkins, M.E., Some conditions for l-transitivity, Discrete Mathematics 109 (1992) 289-296. Every l-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 vertextransitive, edge-transitive graph to be l-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 l-transitive.

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