Paired-Domination in Grid Graphs.
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...
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ndltd-ETSU-oai-dc.etsu.edu-etd-11812019-05-16T04:45:29Z Paired-Domination in Grid Graphs. Proffitt, Kenneth Eugene 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. 2001-05-01T07:00:00Z text application/pdf https://dc.etsu.edu/etd/131 https://dc.etsu.edu/cgi/viewcontent.cgi?article=1181&context=etd Copyright by the authors. Electronic Theses and Dissertations Digital Commons @ East Tennessee State University paired-domination grid graphs domination Physical Sciences and Mathematics |
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paired-domination grid graphs domination Physical Sciences and Mathematics |
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paired-domination grid graphs domination Physical Sciences and Mathematics Proffitt, Kenneth Eugene Paired-Domination in Grid Graphs. |
description |
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. |
author |
Proffitt, Kenneth Eugene |
author_facet |
Proffitt, Kenneth Eugene |
author_sort |
Proffitt, Kenneth Eugene |
title |
Paired-Domination in Grid Graphs. |
title_short |
Paired-Domination in Grid Graphs. |
title_full |
Paired-Domination in Grid Graphs. |
title_fullStr |
Paired-Domination in Grid Graphs. |
title_full_unstemmed |
Paired-Domination in Grid Graphs. |
title_sort |
paired-domination in grid graphs. |
publisher |
Digital Commons @ East Tennessee State University |
publishDate |
2001 |
url |
https://dc.etsu.edu/etd/131 https://dc.etsu.edu/cgi/viewcontent.cgi?article=1181&context=etd |
work_keys_str_mv |
AT proffittkennetheugene paireddominationingridgraphs |
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1719187826682101760 |