This paper discusses a distance guarding concept on triangulation graphs, which can be associated with distance domination and distance vertex cover. We show how these subjects are interconnected and provide tight bounds for any n-vertex maximal outerplanar graph: the 2d-guarding number, g_{ 2d}(n) = n/5; the 2d-distance domination number, gamma_{ 2d}(n) = n/5; and the 2d-distance vertex cover number, beta_{ 2d}(n) = n/4.
Categories: cs.CG