Abstract
We propose the conjecture that the domination number γ(G) of a Δ-regular graph G with Δ≥1 is always at most its edge domination number γe(G), which coincides with the domination number of its line graph. We prove that γ(G)≤1+2(Δ−1)Δ2Δγe(G) for general Δ≥1, and γ(G)≤76−1204γe(G) for Δ=3. Furthermore, we verify our conjecture for cubic claw-free graphs.
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