Defensive alliances are a way of using graphs to model the defense of resources (people, buildings, countries, etc.) against attacks where the number of potential attackers against each resource is known. The initial study of defensive alliances focused on questions of minimal defensive alliances in a graph and the minimum possible size of a defensive alliance in a graph, but in order to apply defensive alliances in modeling real-world situations, additional considerations are important. In particular, since each vertex in a defensive alliance represents some real-world object that has a cost associated with remaining in the defensive alliance, it is important to consider the value each vertex adds to the defensive alliance. In this thesis we consider a method of assessing the efficiency of a defensive alliance, including the special case of secure sets.
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Master of Science (M.S.)
College of Sciences
Length of Campus-only Access
Masters Thesis (Open Access)
Dissertations, Academic -- Sciences, Sciences -- Dissertations, Academic
Worley, George II, "Finding Dud Vertices In Defensive Alliances And Secure Sets Using Computational Tools" (2011). Electronic Theses and Dissertations, 2004-2019. 1815.