The Alliance Problem on Trees and Star Networks

• Main Authors: Cheng Ju Hsu, 許呈如
• Other Authors: Yue-Li Wang
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/99352616712943158658

博士 === 國立臺灣科技大學 === 資訊管理系 === 97 === The alliance problem is a relatively new concept in graph theory and has many interesting and practical variations. Global defensive alliance problem and security problem are two representative problems for showing usefulness to this research field. A lot of graph theorists have much been attracted by these two alliance related problems. This dissertation discusses global defensive alliance problem and security problem on two well-known interconnection networks, namely trees and star networks. This dissertation focuses on the characteristics of trees and star networks and finds useful properties for solving aforementioned problems. The first subject of this dissertation is to find a critical global defensive alliances on star networks. The result is helpful to derive an upper bound to the size of the minimum global (strong) defensive alliances in star networks. The second subject of this dissertation is to propose an algorithm for solving a variation of the security problem. For including a predetermined vertex in a secure set, we are trying to find the minimum secure set on trees and star networks. We use the dynamic programming techniques to find a minimum secure set containing the predetermined vertex on trees. Besides, we also find a secure set with a predetermined vertex on star networks and then establish an upper bound to the dimension of star networks.