Author(s)

Ramy Shaheen, Suhail Mahfud, Khames Almanea

Department of Mathematics, Faculty of Science, Tishreen University, Lattakia, Syria.

A set D of vertices of a graph G = (V, E) is called k-dominating if every vertex v ∈V-D is adjacent to some k vertices of D. The k-domination number of a graph G, γ_k (G), is the order of a smallest k-dominating set of G. In this paper we calculate the k-domination number (for k = 2) of the product of two paths P_m × P_n for m = 1, 2, 3, 4, 5 and arbitrary n. These results were shown an error in the paper [1].

k-Dominating Set, k-Domination Number, 2-Dominating Set, 2-Domination Number, Cartesian Product Graphs, Paths

Shaheen, R. , Mahfud, S. and Almanea, K. (2017) On the 2-Domination Number of Complete Grid Graphs. Open Journal of Discrete Mathematics, 7, 32-50. doi: 10.4236/ojdm.2017.71004.