Bounds on Total Domination Subdivision Numbers.
The domination subdivision number of a graph is the minimum number of edges that must be subdivided in order to increase the domination number of the graph. Likewise, the total domination subdivision number is the minimum number of edges that must be subdivided in order to increase the total dominat...
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Digital Commons @ East Tennessee State University
2003
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ndltd-ETSU-oai-dc.etsu.edu-etd-18952019-05-16T04:47:32Z Bounds on Total Domination Subdivision Numbers. Hopkins, Lora Shuler The domination subdivision number of a graph is the minimum number of edges that must be subdivided in order to increase the domination number of the graph. Likewise, the total domination subdivision number is the minimum number of edges that must be subdivided in order to increase the total domination number. First, this thesis provides a complete survey of established bounds on the domination subdivision number and the total domination subdivision number. Then in Chapter 4, new results regarding bounds on the total domination subdivision number are given. Finally, a characterization of the total domination subdivision number of caterpillars is presented in Chapter 5. 2003-05-03T07:00:00Z text application/pdf https://dc.etsu.edu/etd/738 https://dc.etsu.edu/cgi/viewcontent.cgi?article=1895&context=etd Copyright by the authors. Electronic Theses and Dissertations Digital Commons @ East Tennessee State University Total domination number Domination number Total domination subdivision number Domination subdivision number Physical Sciences and Mathematics |
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Total domination number Domination number Total domination subdivision number Domination subdivision number Physical Sciences and Mathematics |
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Total domination number Domination number Total domination subdivision number Domination subdivision number Physical Sciences and Mathematics Hopkins, Lora Shuler Bounds on Total Domination Subdivision Numbers. |
| description |
The domination subdivision number of a graph is the minimum number of edges that must be subdivided in order to increase the domination number of the graph. Likewise, the total domination subdivision number is the minimum number of edges that must be subdivided in order to increase the total domination number. First, this thesis provides a complete survey of established bounds on the domination subdivision number and the total domination subdivision number. Then in Chapter 4, new results regarding bounds on the total domination subdivision number are given. Finally, a characterization of the total domination subdivision number of caterpillars is presented in Chapter 5. |
| author |
Hopkins, Lora Shuler |
| author_facet |
Hopkins, Lora Shuler |
| author_sort |
Hopkins, Lora Shuler |
| title |
Bounds on Total Domination Subdivision Numbers. |
| title_short |
Bounds on Total Domination Subdivision Numbers. |
| title_full |
Bounds on Total Domination Subdivision Numbers. |
| title_fullStr |
Bounds on Total Domination Subdivision Numbers. |
| title_full_unstemmed |
Bounds on Total Domination Subdivision Numbers. |
| title_sort |
bounds on total domination subdivision numbers. |
| publisher |
Digital Commons @ East Tennessee State University |
| publishDate |
2003 |
| url |
https://dc.etsu.edu/etd/738 https://dc.etsu.edu/cgi/viewcontent.cgi?article=1895&context=etd |
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AT hopkinslorashuler boundsontotaldominationsubdivisionnumbers |
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1719187865155403776 |