Abstract
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. Combin. Theory 3 (1967) 215–232) that a regular edge-transitive graph of order 2p or 2p 2 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 8p is symmetric, and then all such graphs are classified.
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Alaeiyan, M., Hosseinipoor, M.K. Classifying cubic edge-transitive graphs of order 8p . Proc Math Sci 119, 647–653 (2009). https://doi.org/10.1007/s12044-009-0056-6
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DOI: https://doi.org/10.1007/s12044-009-0056-6