Let G be a permutation group on a set Omega, and recall that a base for G is a subset of Omega such that its pointwise stabiliser is trivial. In a recent paper, Burness and Giudici introduced the Saxl graph of G, denoted Sigma(G), with vertex set Omega and two vertices adjacent if and only if they form a base for G. If G is transitive, then Sigma(G) is vertex-transitive, and it is natural to consider its valency (which we refer to as the valency of G). In this paper, we present a general method for computing the valency of any finite transitive group, and we use it to calculate the exact valency of every primitive group with stabiliser a Frobenius group with cyclic kernel. As an application, we calculate the valency of every almost simple primitive group with an alternating socle and soluble stabiliser, and we use this to extend results of Burness and Giudici on almost simple primitive groups with prime-power or odd valency.
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