Domination number of Cartesian product through space projections

In 1968, Vizing conjectured that for every pair of graphs X and Y, the inequality γ(X Y ) ≥ γ(X)γ(Y ) holds, where γ stands for the domination number and X Y is the Cartesian product of X and Y.In a breakthrough result, Clark and Suen [Electron.J. Combin.7 (2000) #N4] proved that γ(X Y ) ≥ 1 2 γ(X)γ(Y ).In this paper, a lower bound for γ(X Y Z) is obtained using projections in the space.It is shown how the obtained bound implies the mentioned result of Clark and Suen.