Allagan, Julian A. D. Contributor (Department of Mathematics, Computer Science, and Engineering Technology)
Description
Given a simple undirected graph G = (V;E), a -set also known as dominating setis a subset S V such that for any vertex v 2 V , either v 2 S or a neighbor u of v is in S. Given G, the size of its -set, denoted by , is its domination number and the dominion of G, denoted by , counts the number of its -sets. The former is a well-studied concept while the latter is new. Each parameter accesses the reliabilityand the vulnerability of a network system when exposed to attacks. In this thesis,we introduce basic notions and topology of several graphs. For each such graph, wefound and proved the aforementioned parameters while presenting several activitieswith solutions.
Date
2020-01-01
Department/Academic Units
Department of Mathematics, Computer Science, and Engineering Technology
