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Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
5-2001
Committee Chair or Co-Chairs
Teresa W. Haynes
Committee Members
Debra J. Knisley, Janice Huang
Abstract
Every graph G = (V, E) has a dominating set S ⊆ V(G) such that any vertex not in S is adjacent to a vertex in S. We define a paired-dominating set S to be a dominating set S = {v1, v2,..., v2t-1, v2t} where M = {v1v2, v3v4, ..., v2t-1v2t} is a perfect matching in 〈S〉, the subgraph induced by S. The domination number of a graph G is the smallest cardinality of any dominating set of G, and the paired-domination number is the smallest cardinality of any paired-dominating set. Determining the domination number for grid graphs is a well-known open problem in graph theory. Not surprisingly, determining the paired-domination number for grid graphs is also a difficult problem. In this thesis, we survey past research in domination, paired-domination and grid graphs to obtain background for our study of paired-domination in grid graphs. We determine the paired-domination number for grid graphs Gr,c where r ∈ {2,3}, for infinite dimensional grid graphs, and for the complement of a grid graph.
Document Type
Thesis - restricted
Recommended Citation
Proffitt, Kenneth Eugene, "Paired-Domination in Grid Graphs." (2001). Electronic Theses and Dissertations. Paper 131. https://dc.etsu.edu/etd/131
Copyright
Copyright by the authors.