On the 2-Domination Number of Complete Grid Graphs

• 作者: Khames Almanea Ramy Shaheen Suhail Mahfud
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: k-Dominating SET K-DOMINATION NUMBER 2-Dominating SET 2-Domination NUMBER CARTESIAN Product Graphs PATHS
• 年，卷（期）: 2017,（1）
• 页码范围: 32-50
• 页数: 19页
• 分类号: O1

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].