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Zbl 0939.05047
Praeger, Cheryl E.
Finite normal edge-transitive Cayley graphs. (English)
[J] Bull. Aust. Math. Soc. 60, No.2, 207-220 (1999). ISSN 0004-9727

More than one definition has been used for the word ``normal'' as applied to Cayley graphs, but several authors have recently used the following definition: a Cayley graph for a group $G$ is said to be ``normal'' if $G$ (in its regular action) is normalized by the full automorphism group of the graph. In the present paper the author defines a Cayley graph to be ``normal edge-transitive'' if its automorphism group contains a subgroup which both normalizes $G$ and acts transitively on the edges. (Throughout the paper the author considers both ``graphs,'' by which she means directed graphs, and ``undirected graphs.'') The author suggests that these form a subfamily of central importance to analyzing the family of all Cayley graphs for a given group. For example, she proves that any Cayley graph for $G$ is an edge-disjoint union of normal edge-transitive Cayley graphs for $G$. The author also proves results on quotients of Cayley graphs (describing when these are Cayley graphs for a quotient group, etc.), and on constructing all normal edge-transitive Cayley graphs having a given normal edge-transitive Cayley graph as a quotient. The paper concludes with a sample theorem about the full automorphism groups of normal edge-transitive Cayley graphs for finite simple groups.
[A.J.Goodman (Rolla)]

MSC 2000:: *05C25 Graphs and groups
20B25 Finite automorphism groups of miscellaneous structures

Keywords: Cayley graph; edge-transitive; quotients; automorphism group

Cited in: Zbl 1124.05040 Zbl 1109.05048

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