摘要
In this paper, we investigate semisymmetric graphs of order 6p2 and of prime valency. First, we give a classification of the quasiprimitive permutation groups of degree dividing 3p2, and then, on the basis of the classification result, we prove that, for primes k and p, a connected graph Γ of order 6p2 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.
In this paper, we investigate semisymmetric graphs of order 6p2 and of prime valency. First, we give a classification of the quasiprimitive permutation groups of degree dividing 3p2, and then, on the basis of the classification result, we prove that, for primes k and p, a connected graph Γ of order 6p2 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.
