On dominating sets of maximal outerplanar graphs

A dominating set of a graph is a set SS of vertices such that every vertex in the graph is either in SS or is adjacent to a vertex in SS. The domination number of a graph GG, denoted γ(G)γ(G), is the minimum cardinality of a dominating set of GG. We show that if GG is an nn-vertex maximal outerplanar graph, then γ(G)≤(n+t)/4γ(G)≤(n+t)/4, where tt is the number of vertices of degree 22 in GG. We show that this bound is tight for all t≥2t≥2. Upper-bounds for γ(G)γ(G) are known for a few classes of graphs.