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LOCALLY PRIMITIVE GRAPHS OF PRIME-POWER ORDER

Part of: Graph theory

Published online by Cambridge University Press:  01 February 2009

CAI HENG LI ,
JIANGMIN PAN  and
LI MA
CAI HENG LI*
Affiliation:
School of Mathematics and Statistics, The University of Western Australia, Crawley, WA 6009, Australia (email: li@maths.uwa.edu.au)
JIANGMIN PAN
Affiliation:
Department of Mathematics, Yunnan University, Kunming 650031, PR China (email: jmpan@ynu.edu.cn)
LI MA
Affiliation:
Department of Mathematics, Yunnan University, Kunming 650031, PR China
*
✉For correspondence; e-mail: li@maths.uwa.edu.au
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Abstract

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Let Γ be a finite connected undirected vertex transitive locally primitive graph of prime-power order. It is shown that either Γ is a normal Cayley graph of a 2-group, or Γ is a normal cover of a complete graph, a complete bipartite graph, or Σ×l, where Σ=Kpm with p prime or Σ is the Schläfli graph (of order 27). In particular, either Γ is a Cayley graph, or Γ is a normal cover of a complete bipartite graph.

Keywords

locally primitive graphsCayley graphscovers

MSC classification

Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 1 , February 2009 , pp. 111 - 122
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

This work forms a part of the PhD project of Jiangmin Pan. It was partially supported by a NNSF and an ARC Discovery Project Grant.

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