Following partially a suggestion by Pyber, we prove that the diameter of product non-abelian finite simple groups is bounded linearly maximum its factors. For completeness, include case abelian factors and give explicit constants in all bounds.
Building on earlier results for regular maps and orientably chiral maps, we classify the non-abelian finite simple groups arising as automorphism of in each 14 Graver–Watkins classes edge-transitive maps.