Double hop dominating sets in graphs.

Let G = (V , E) be a connected graph of order n ≥ 4. A subset S ⊆ V (G) is a double hop dominating set (or a double 2 -step dominating set) if | N G [ v , 2 ] ∩ S | ≥ 2 , where N G [ v , 2 ] = { v } ∪ { w ∈ V (G) : d G (v , w) = 2 } , for each v ∈ V (G). The smallest cardinality of a double hop dominating set of G , denoted by γ × 2 h (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. [ABSTRACT FROM AUTHOR]