Conjecture that γ(G) ≤ γ_e(G) for Δ-regular graphs G, with proved bound γ(G) ≤ (1 + 2(Δ-1)/(Δ 2^Δ)) γ_e(G), tighter bound for Δ=3, and verification for cubic claw-free graphs.
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Domination versus edge domination
Conjecture that γ(G) ≤ γ_e(G) for Δ-regular graphs G, with proved bound γ(G) ≤ (1 + 2(Δ-1)/(Δ 2^Δ)) γ_e(G), tighter bound for Δ=3, and verification for cubic claw-free graphs.