Classifying Cubic Semisymmetric Graphs of Order 18 p
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Authors: | A A Talebi N Mehdipoor |
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Institution: | 1. Department of Mathematics, University of Mazandaran, Babolsar, Iran
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Abstract: | A graph X is said to be G-semisymmetric if it is regular and there exists a subgroup G of A := Aut (X) acting transitively on its edge set but not on its vertex set. In the case of G = A, we call X a semisymmetric graph. Let p be a prime. It was shown by Folkman (J Comb Theory 3:215–232, 1967) that a regular edge-transitive graph of order 2p or 2p 2 is necessarily vertex-transitive. The smallest semisymmetric graph is the Folkman graph. In this study, we classify all connected cubic semisymmetric graphs of order 18p n , where p is a prime and \({n \geq 1}\) . |
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