Convex dominating sets in maximal outerplanar graphs

Abstract

In this paper, we study the concept of convex domination in maximal outerplanar graphs. For this class of graphs, we discuss several properties of this domination parameter, in particular, we provide upper bounds on the convex domination number and study effects on the convex domination number when a maximal outerplanar graph is modified by flipping a diagonal. We also propose a linear time algorithm for computing a minimum convex dominating set in a given maximal outerplanar graph. In addition, we consider the concept of convex guard sets in maximal outerplanar graphs and simple polygons.