Journal of the Australian Mathematical Society
- Journal of the Australian Mathematical Society / Volume 71 / Issue 02 / October 2001, pp 223-232
- Copyright © Australian Mathematical Society 2001
- DOI: http://dx.doi.org/10.1017/S144678870000286X (About DOI), Published online: 09 April 2009
Research Article
Automorphisms of Cayley graphs of metacyclic groups of prime-power order
Caiheng Lia1 and Hyo-Seob Sima2
a1 Department of Mathematics and Statistics, The University of Western Australia, Nedlands WA 6907, Australia e-mail: li@maths.uwa.edu.au
a2 Division of Mathematical Sciences, Pukyong National University, Pusan 608-737, Korea e-mail: hism@pknu.ac.kr
Abstract
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.
(Received October 17 2000)
2000 Mathematics subject classification
- primary 05C25;
- 20B25
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