Connected minimum secure-dominating sets in grids. Issue 3 (1st December 2017) - Barnett, Johnathan; Blumenthal, Adam; Johnson, Peter; Jones, Cadavious; Matzke, Ryan; Mujuni, Egbert
Abstract: For any (finite simple) graph G the secure domination number of G satisfies γ s ( G ) ≥ | V ( G ) | 2 . Here we find a secure-dominating set S in G such that | S | = ⌈ | V ( G ) | 2 ⌉ in all cases when G is a grid, and in the majority of cases when G is a cylindrical or toroidal grid. In all such cases, S satisfies the additional requirement that G [ S ] is connected. We make note that the concept of secure-dominating sets considered in this paper is quite different from the other secure domination currently of interest. 1