On the 2-Domination Number of Complete Grid Graphs

作     者：Ramy Shaheen Suhail Mahfud Khames Almanea 

作者机构：Department of Mathematics Faculty of Science Tishreen University Lattakia Syria 

出 版 物：《Open Journal of Discrete Mathematics》 (离散数学期刊（英文）)

年 卷 期：2017年第7卷第1期

页      面：32-50页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：k-Dominating Set k-Domination Number 2-Dominating Set 2-Domination Number Cartesian Product Graphs Paths 

摘      要：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].