a b s t r a c tLet G be a graph and S ⊆ V (G). For each vertex u ∈ S and for eachThe smallest cardinality of an exponential dominating set is the exponential domination number, γ e (G). In this paper, we prove: (i) that if G is a connected graph of diameter d, then γ e (G) ≥ (d + 2)/4, and, (ii) that if G is a connected graph of order n, then γ e (G) ≤ 2 5 (n + 2).
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