Let be a graph of order n. with vertices and edges .
A set D of vertices of a graph is called 2- dominating if every vertex has at least two neighbors in D. let denotes The 2- domination number of a graph G, , is the order of a smallest 2- dominatin
g set of G. In this paper, we found lower and upper bounds of 2- domination number of the cartesian product of two paths for m=6,7 and arbitrary n.
