Domination and Dominion of Some Graphs

ECSU Author/Contributor (non-ECSU co-authors, if there are any, appear on document)
Juston Blue, student (Creator)
Julian A. D. Allagan , Associate Professor (Contributor)
Elizabeth City State University (ECSU )
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Abstract: 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.

Additional Information

Language: English
Date: 2020
domination graphs

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