Domination ratio of integer distance digraphs

Abstract An integer distance digraph is the Cayley graph Γ ( Z , S ) of the additive group Z of all integers with respect to some finite subset S ⊆ Z . The domination ratio of Γ ( Z , S ) is the minimum density of a dominating set in Γ ( Z , S ) . We establish some basic results on the domination ratio of Γ ( Z , S ) and precisely determine it when S = { s , t } with s dividing t .