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Classifying Cubic Semisymmetric Graphs of Order 18 p n

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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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Authors and Affiliations

  1. Department of Mathematics, University of Mazandaran, Babolsar, Iran

    A. A. Talebi & N. Mehdipoor

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  1. A. A. Talebi
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  2. N. Mehdipoor
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Correspondence to A. A. Talebi.

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Talebi, A.A., Mehdipoor, N. Classifying Cubic Semisymmetric Graphs of Order 18 p n . Graphs and Combinatorics 30, 1037–1044 (2014). https://doi.org/10.1007/s00373-013-1318-8

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  • DOI: https://doi.org/10.1007/s00373-013-1318-8

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