Maximal outerplanar graphs satisfy γ_{×2}(G) ≤ (n + k)/2 where k is the number of distant consecutive pairs on the outer cycle.
Tokunaga, Dominating sets of maximal outerplanar graphs, Discrete Applied Mathematics 161 (2013) 3097–3099
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An Upper Bound for the Double Domination Number in Maximal Outerplanar Graphs
Maximal outerplanar graphs satisfy γ_{×2}(G) ≤ (n + k)/2 where k is the number of distant consecutive pairs on the outer cycle.