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Semisymmetric graphs of order 6p 2 and prime valency

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Abstract

In this paper, we investigate semisymmetric graphs of order 6p 2 and of prime valency. First, we give a classification of the quasiprimitive permutation groups of degree dividing 3p 2, and then, on the basis of the classification result, we prove that, for primes k and p, a connected graph Γ of order 6p 2 and valency k is semisymmetric if and only if k = 3 and either Γ is the Gray graph, or p ≠ 1 (mod 6) and Γ is isomorphic to one known graph.

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  1. Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin, 300071, China

    Hua Han & ZaiPing Lu

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  1. Hua Han
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  2. ZaiPing Lu
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Correspondence to ZaiPing Lu.

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Han, H., Lu, Z. Semisymmetric graphs of order 6p 2 and prime valency. Sci. China Math. 55, 2579–2592 (2012). https://doi.org/10.1007/s11425-012-4424-9

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  • DOI: https://doi.org/10.1007/s11425-012-4424-9

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