Weakly convex and convex domination numbers

Abstract

Two new domination parameters for a connected graph \(G\): the weakly convex domination number of \(G\) and the convex domination number of \(G\) are introduced. Relations between these parameters and the other domination parameters are derived. In particular, we study for which cubic graphs the convex domination number equals the connected domination number.

Keywords

• dominating set
• connected domination number
• distance
• isometric set
• convex set