Properties of Small Ordered Graphs Whose Vertices are Weighted by Their Degree
Graphs can effectively model biomolecules, computer systems, and other applications. A weighted graph is a graph in which values or labels are assigned to the edges of the graph. However, in this thesis, we assign values to the vertices of the graph rather than the edges and we modify several standa...
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ndltd-ETSU-oai-dc.etsu.edu-etd-37742019-05-16T04:45:29Z Properties of Small Ordered Graphs Whose Vertices are Weighted by Their Degree Blalock, Constance M Graphs can effectively model biomolecules, computer systems, and other applications. A weighted graph is a graph in which values or labels are assigned to the edges of the graph. However, in this thesis, we assign values to the vertices of the graph rather than the edges and we modify several standard graphical measures to incorporate these vertex weights. In particular, we designate the degree of each vertex as its weight. Previous research has not investigated weighting vertices by degree. We find the vertex weighted domination number in connected graphs, beginning with trees, and we define how weighted vertices can affect eccentricity, independence number, and connectivity. 2014-08-01T07:00:00Z text application/pdf https://dc.etsu.edu/etd/2416 https://dc.etsu.edu/cgi/viewcontent.cgi?article=3774&context=etd Copyright by the authors. Electronic Theses and Dissertations Digital Commons @ East Tennessee State University graph theory weighted graphs vertex weight Mathematics Physical Sciences and Mathematics |
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graph theory weighted graphs vertex weight Mathematics Physical Sciences and Mathematics |
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graph theory weighted graphs vertex weight Mathematics Physical Sciences and Mathematics Blalock, Constance M Properties of Small Ordered Graphs Whose Vertices are Weighted by Their Degree |
description |
Graphs can effectively model biomolecules, computer systems, and other applications. A weighted graph is a graph in which values or labels are assigned to the edges of the graph. However, in this thesis, we assign values to the vertices of the graph rather than the edges and we modify several standard graphical measures to incorporate these vertex weights. In particular, we designate the degree of each vertex as its weight. Previous research has not investigated weighting vertices by degree. We find the vertex weighted domination number in connected graphs, beginning with trees, and we define how weighted vertices can affect eccentricity, independence number, and connectivity. |
author |
Blalock, Constance M |
author_facet |
Blalock, Constance M |
author_sort |
Blalock, Constance M |
title |
Properties of Small Ordered Graphs Whose Vertices are Weighted by Their Degree |
title_short |
Properties of Small Ordered Graphs Whose Vertices are Weighted by Their Degree |
title_full |
Properties of Small Ordered Graphs Whose Vertices are Weighted by Their Degree |
title_fullStr |
Properties of Small Ordered Graphs Whose Vertices are Weighted by Their Degree |
title_full_unstemmed |
Properties of Small Ordered Graphs Whose Vertices are Weighted by Their Degree |
title_sort |
properties of small ordered graphs whose vertices are weighted by their degree |
publisher |
Digital Commons @ East Tennessee State University |
publishDate |
2014 |
url |
https://dc.etsu.edu/etd/2416 https://dc.etsu.edu/cgi/viewcontent.cgi?article=3774&context=etd |
work_keys_str_mv |
AT blalockconstancem propertiesofsmallorderedgraphswhoseverticesareweightedbytheirdegree |
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1719188249816072192 |