On Signed Domination of Grid Graph

• 作者: Mazen Mostafa
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: Grid Graph Cartesian Product Signed Dominating Function Signed Domination Number
• 年，卷（期）: 2020,（4）
• 页码范围: 96-112
• 页数: 17页
• 分类号: O15

摘要

Let <em>G</em>(<em>V</em>, <em>E</em>) be a finite connected simple graph with vertex set <em>V</em>(<em>G</em>). A function is a signed dominating function <em>f </em>: <em style="white-space:normal;">V</em><span style="white-space:normal;">(</span><em style="white-space:normal;">G</em><span style="white-space:normal;">)</span><span style="white-space:nowrap;">→{<span style="white-space:nowrap;"><span style="white-space:nowrap;">&minus;</span></span>1,1}</span> if for every vertex <em>v</em> <span style="white-space:nowrap;">∈</span> <em>V</em>(<em>G</em>), the sum of closed neighborhood weights of <em>v</em> is greater or equal to 1. The signed domination number <em>γ</em>_s(<em>G</em>) of <em>G</em> is the minimum weight of a signed dominating function on <em>G</em>. In this paper, we calculate the signed domination numbers of the Cartesian product of two paths <em>P</em>_<em>m</em> and <em>P</em>_<em>n</em> for <em>m</em> = 6, 7 and arbitrary <em>n</em>.