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Automorphisms of Cayley graphs of metacyclic groups of prime-power order

Part of: Graph theory Permutation groups

Published online by Cambridge University Press:  09 April 2009

Caiheng Li  and
Hyo-Seob Sim
Caiheng Li
Affiliation:
Department of Mathematics and Statistics, The University of Western Australia, Nedlands WA 6907, Australia e-mail: li@maths.uwa.edu.au
Hyo-Seob Sim
Affiliation:
Division of Mathematical Sciences, Pukyong National University, Pusan 608-737, Korea e-mail: hism@pknu.ac.kr
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Abstract

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This paper inverstigates the automorphism groups of Cayley graphs of metracyclic p-gorups. A characterization is given of the automorphism groups of Cayley grahs of a metacyclic p-group for odd prime p. In particular, a complete determiniation of the automophism group of a connected Cayley graph with valency less than 2p of a nonabelian metacyclic p-group is obtained as a consequence. In subsequent work, the result of this paper has been applied to solve several problems in graph theory.

MSC classification

Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 2 , October 2001 , pp. 223 - 232
Copyright
Copyright © Australian Mathematical Society 2001

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