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General bounds are presented for the diameters of orbital graphs of finiteaffine primitive permutation groups. For example, it is proved that the orbitaldiameter of a finite affine primitive permutation group with a nontrivial pointstabilizer $ H \leq \mathrm{GL}(V) $, where the vector space $ V $ hasdimension $ d $ over the prime field, can be bounded in terms of $ d $ and $\log |V| / \log |H| $ only. Several infinite families of affine primitivepermutation groups with large orbital diameter are constructed. The results areindependent from the classification of finite simple groups.

Bounds for the diameters of orbital graphs of affine groups