Digital Commons Network^™

Global Secure Sets Of Trees And Grid-Like Graphs, Yiu Yu Ho

Electronic Theses and Dissertations

Let G = (V, E) be a graph and let S ⊆ V be a subset of vertices. The set S is a defensive alliance if for all x ∈ S, |N[x] ∩ S| ≥ |N[x] − S|. The concept of defensive alliances was introduced in [KHH04], primarily for the modeling of nations in times of war, where allied nations are in mutual agreement to join forces if any one of them is attacked. For a vertex x in a defensive alliance, the number of neighbors of x inside the alliance, plus the vertex x, is at least the number …