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CUBIC EDGE-TRANSITIVE GRAPHS OF ORDER 8p2

Part of: Permutation groups Graph theory

Published online by Cambridge University Press:  01 April 2008

MEHDI ALAEIYAN  and
MOHSEN GHASEMI
MEHDI ALAEIYAN*
Affiliation:
Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran (email: [email protected])
MOHSEN GHASEMI
Affiliation:
Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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A simple undirected graph is said to be semisymmetric if it is regular and edge-transitive but not vertex-transitive. Let p be a prime. It was shown by Folkman [J. Folkman, ‘Regular line-symmetric graphs’, J. Combin. Theory3 (1967), 215–232] that a regular edge-transitive graph of order 2p or 2p2 is necessarily vertex-transitive. In this paper an extension of his result in the case of cubic graphs is given. It is proved that every cubic edge-transitive graph of order 8p2 is vertex-transitive.

Keywords

semisymmetric graphssymmetric graphsregular coverings

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
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 2 , April 2008 , pp. 315 - 323
Copyright
Copyright © 2008 Australian Mathematical Society

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