The Structure of Automorphism Groups of Cayley Graphs and Maps

Authors:
Robert Jajcay
Affiliations:
Department of Mathematics and Computer Science, Indiana State University, Terre Haute, IN 47809, USA. jajcay@laurel.indstate.edu
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2000

Citing 6
Cited 3

Topological graph theory

Topological graph theory
Regular maps from Cayley graphs, part 1: balanced Cayley maps

Discrete Mathematics - Algebraic graph theory; a volume dedicated to Gert Sabidussi
Automorphism groups of Cayley maps

Journal of Combinatorial Theory Series B
Regular maps from Cayley graphs II: antibalanced Cayley maps

Proceedings of the first Malta conference on Graphs and combinatorics
On a new product of groups

European Journal of Combinatorics
Characterization and construction of Cayley graphs admitting regular Cayley maps

Discrete Mathematics

Skew-morphisms of regular Cayley maps

Discrete Mathematics - Algebraic and topological methods in graph theory
Cayley maps

Journal of Combinatorial Theory Series B
Automorphisms of augmented cubes

International Journal of Computer Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

The automorphism groups iAut(iC(iG, iX)) and iAut(iCM(iG, iX, ip)) of a Cayley graph iC(iG, iX) and a Cayley map iCM(iG, iX, ip) both contain an isomorphic copy of the underlying group iG acting via left translations. In our paper, we show that both automorphism groups are rotary extensions of the group iG by the stabilizer subgroup of the vertex 1iG. We use this description to derive necessary and sufficient conditions to be satisfied by a finite group in order to be the (full) automorphism group of a Cayley graph or map and classify all the finite groups that can be represented as the (full) automorphism group of some Cayley graph or map.