On dominating sets of maximal outerplanar graphs

A dominating set of a graph is a set S of vertices such that every vertex in the graph is either in S or is adjacent to a vertex in S. The domination number of a graph G, denoted γ (G), is theminimum cardinality of a dominating set ofG. We show that ifG is an n-vertexmaximal outerplanar graph, then γ (G) ≤ (n + t)/4, where t is the number of vertices of degree 2 in G. We show that this bound is tight for all t ≥ 2. Upper-bounds for γ (G) are known for a few classes of graphs. © 2012 Elsevier B.V. All rights reserved.