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TETRAVALENT s-TRANSITIVE GRAPHS OF ORDER TWICE A PRIME POWER

Part of: Graph theory

Published online by Cambridge University Press:  08 April 2010

JIN-XIN ZHOU  and
YAN-QUAN FENG
JIN-XIN ZHOU*
Affiliation:
Department of Mathematics, Beijing Jiaotong University, Beijing 100044, PR China (email: 05118322@bjtu.edu.cn, jxzhou@bjtu.edu.cn)
YAN-QUAN FENG
Affiliation:
Department of Mathematics, Beijing Jiaotong University, Beijing 100044, PR China (email: yqfeng@bjtu.edu.cn)
*
✉For correspondence; e-mail: jxzhou@bjtu.edu.cn
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Abstract

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A graph is s-transitive if its automorphism group acts transitively on s-arcs but not on (s+1)-arcs in the graph. Let X be a connected tetravalent s-transitive graph of order twice a prime power. In this paper it is shown that s=1,2,3 or 4. Furthermore, if s=2, then X is a normal cover of one of the following graphs: the 4-cube, the complete graph of order 5, the complete bipartite graph K5,5 minus a 1-factor, or K7,7 minus a point-hyperplane incidence graph of the three-dimensional projective geometry PG(2,2); if s=3, then X is a normal cover of the complete bipartite graph of order 4; if s=4, then X is a normal cover of the point-hyperplane incidence graph of the three-dimensional projective geometry PG(2,3). As an application, we classify the tetravalent s-transitive graphs of order 2p2 for prime p.

Keywords

s-transitive graphsymmetric graphCayley graph

MSC classification

Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 88 , Issue 2 , April 2010 , pp. 277 - 288
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

The authors are grateful for the support of the National Natural Science Foundation of China (10871021, 10901015), the Specialized Research Fund for the Doctoral Program of Higher Education in China (20060004026), and the Science and Technology Foundation of Beijing Jiaotong University (2008RC037).

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