Domination and Eternal Domination of Jahangir Graph

• 作者: Ali Kassem Mohammad Assaad Ramy Shaheen
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: Jahangir GRAPH GRAPH PROTECTION DOMINATION NUMBER ETERNAL DOMINATION
• 年，卷（期）: 2019,（3）
• 页码范围: 68-81
• 页数: 14页
• 分类号: O1

摘要

In the eternal dominating set problem, guards form a dominating set on a graph and at each step, a vertex is attacked. We consider the “all guards move” of the eternal dominating set problem. In which one guard has to move to the attacked vertex and all the remaining guards are allowed to move to an adjacent vertex or stay in their current position after each attack. If the new formed set of guards is still a dominating set of the graph then we successfully defended the attack. Our goal is to find the minimum number of guards required to eternally protect the graph. We call this number the m-eternal domination number and we denote it by . In this paper we find the eternal domination number of Jahangir graph Js,m for s=2,3 and arbitrary m. We also find the domination number for J3,m .