# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Finite normal edge-transitive Cayley graphs. (English) Zbl 0939.05047
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.

##### MSC:
 05C25 Graphs and abstract algebra 20B25 Finite automorphism groups of miscellaneous structures
##### Keywords:
Cayley graph; edge-transitive; quotients; automorphism group