On the Signed Domination Number of the Cartesian Product of Two Directed Cycles

• 作者: Ramy Shaheen
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: Directed GRAPH Directed CYCLE CARTESIAN Product SIGNED Dominating Function SIGNED DOMINATION NUMBER
• 年，卷（期）: 2015,（3）
• 页码范围: 54-64
• 页数: 11页
• 分类号: O1

摘要

Let D be a finite simple directed graph with vertex set V(D) and arc set A(D). A function ?is called a signed dominating function (SDF) if ?for each vertex . The weight ?of f is defined by . The signed domination number of a digraph D is . Let Cm × Cn denotes the cartesian product of directed cycles of length m and n. In this paper, we determine the exact values of gs(Cm × Cn) for m = 8, 9, 10 and arbitrary n. Also, we give the exact value of gs(Cm × Cn) when m, ?(mod 3) and bounds for otherwise.