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Tetravalent vertex-transitive graphs of order 4p

✍ Scribed by Jin-Xin Zhou

Publisher: John Wiley and Sons
Year: 2011
Tongue: English
Weight: 219 KB
Volume: 71
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20653

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✦ Synopsis

A graph is vertex‐transitive if its automorphism group acts transitively on vertices of the graph. A vertex‐transitive graph is a Cayley graph if its automorphism group contains a subgroup acting regularly on its vertices. In this article, the tetravalent vertex‐transitive non‐Cayley graphs of order 4__p__ are classified for each prime p. As a result, there are one sporadic and five infinite families of such graphs, of which the sporadic one has order 20, and one infinite family exists for every prime p>3, two families exist if and only if p≡1 (mod 8) and the other two families exist if and only if p≡1 (mod 4). For each family there is a unique graph for a given order. © 2011 Wiley Periodicals, Inc.

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