TITLE:
On the 2-Domination Number of Complete Grid Graphs
AUTHORS:
Ramy Shaheen, Suhail Mahfud, Khames Almanea
KEYWORDS:
k-Dominating Set, k-Domination Number, 2-Dominating Set, 2-Domination Number, Cartesian Product Graphs, Paths
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.7 No.1,
January
23,
2017
ABSTRACT: 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, γk (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 Pm × Pn for m = 1, 2, 3, 4, 5 and arbitrary n. These results were shown an error in the paper [1].