Distance domination, guarding and covering of maximal outerplanar graphs

In this paper we introduce the notion of distance kk-guarding applied to triangulation graphs, and associate it with distance kk-domination and distance kk-covering. We obtain results for maximal outerplanar graphs when k=2k=2. A set SS of vertices in a triangulation graph TT is a distance 2-guarding set (or 2d2d-guarding set for short) if every face of TT has a vertex adjacent to a vertex of SS. We show that ⌊n5⌋ (respectively, ⌊n4⌋) vertices are sufficient to 2d2d-guard and 2d2d-dominate (respectively, 2d2d-cover) any nn-vertex maximal outerplanar graph. We also show that these bounds are tight.