Bounds on the Distance Two-Domination Number of a Graph

Abstract.

 For a graph G = (V, E), a subset D⊆V(G) is said to be distance two-dominating set in G if for each vertex u∈V−D, there exists a vertex v∈D such that d(u,v)≤2. The minimum cardinality of a distance two-dominating set in G is called a distance two-domination number and is denoted by γ₂(G). In this note we obtain various upper bounds for γ₂(G) and characterize the classes of graphs attaining these bounds.