Double hop dominating sets in graphs

Let G = (V,E) be a connected graph of order n >= 4. A subset S subset of V (G) is a double hop dominating set (or a double 2-step dominating set) if |N-G[v, 2] boolean AND S|>= 2, where NG[v, 2] = {v}boolean OR{w is an element of V (G) : d(G)(v,w) = 2}, for each v is an element of V (G). The smallest cardinality of a double hop dominating set of G, denoted by gamma(h)(x2)(G), is the double hop domination number of G. In this paper, we investigate the concept of double hop dominating sets and study it for graphs resulting from some binary operations.