The Signed Domination Number of Cartesian Product of Two Paths

• 作者: Mazen Mostafa Mohammad Hassan Muhsin Al Hassan
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: PATH CARTESIAN Product SIGNED Dominating Function SIGNED DOMINATION NUMBER
• 年，卷（期）: 2020,（2）
• 页码范围: 45-55
• 页数: 11页
• 分类号: O15

摘要

Let G be a finite connected simple graph with vertex set V(G) and edge set E(G). A function f:V(G) → {1,1} is a signed dominating function if for every vertex v∈V(G), the closed neighborhood of v contains more vertices with function values 1 than with −1. The signed domination number γs(G) of G is the minimum weight of a signed dominating function on G. In this paper, we calculate The signed domination numbers of the Cartesian product of two paths Pm and Pn for m = 3, 4, 5 and arbitrary n.