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A graph Γ is called G -basic if G is quasiprimitive or bi-quasiprimitive on the vertex set of Γ , where G ≤ AutΓ . In this paper, we complete the classification of r -valent arc-transitive basic graphs with order 4p or 4p , where p and r are odd primes.

Prime-valent arc-transitive basic graphs with order 4 p or 4 p 2