Total Domination in Rooted Product Graphs
During the last few decades, domination theory has been one of the most active areas of research within graph theory. Currently, there are more than 4400 published papers on domination and related parameters. In the case of total domination, there are over 580 published papers, and 50 of them concer...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/12/11/1929 |
| _version_ | 1797546954227449856 |
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| author | Abel Cabrera Martínez Juan A. Rodríguez-Velázquez |
| author_facet | Abel Cabrera Martínez Juan A. Rodríguez-Velázquez |
| author_sort | Abel Cabrera Martínez |
| collection | DOAJ |
| description | During the last few decades, domination theory has been one of the most active areas of research within graph theory. Currently, there are more than 4400 published papers on domination and related parameters. In the case of total domination, there are over 580 published papers, and 50 of them concern the case of product graphs. However, none of these papers discusses the case of rooted product graphs. Precisely, the present paper covers this gap in the theory. Our goal is to provide closed formulas for the total domination number of rooted product graphs. In particular, we show that there are four possible expressions for the total domination number of a rooted product graph, and we characterize the graphs reaching these expressions. |
| first_indexed | 2024-03-10T14:37:31Z |
| format | Article |
| id | doaj.art-094dd6fe8f8a49ccbe0d28a068833f6d |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T14:37:31Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-094dd6fe8f8a49ccbe0d28a068833f6d2023-11-20T22:02:44ZengMDPI AGSymmetry2073-89942020-11-011211192910.3390/sym12111929Total Domination in Rooted Product GraphsAbel Cabrera Martínez0Juan A. Rodríguez-Velázquez1Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Av. Països Catalans 26, 43007 Tarragona, SpainDepartament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Av. Països Catalans 26, 43007 Tarragona, SpainDuring the last few decades, domination theory has been one of the most active areas of research within graph theory. Currently, there are more than 4400 published papers on domination and related parameters. In the case of total domination, there are over 580 published papers, and 50 of them concern the case of product graphs. However, none of these papers discusses the case of rooted product graphs. Precisely, the present paper covers this gap in the theory. Our goal is to provide closed formulas for the total domination number of rooted product graphs. In particular, we show that there are four possible expressions for the total domination number of a rooted product graph, and we characterize the graphs reaching these expressions.https://www.mdpi.com/2073-8994/12/11/1929total dominationdominationrooted product graph |
| spellingShingle | Abel Cabrera Martínez Juan A. Rodríguez-Velázquez Total Domination in Rooted Product Graphs Symmetry total domination domination rooted product graph |
| title | Total Domination in Rooted Product Graphs |
| title_full | Total Domination in Rooted Product Graphs |
| title_fullStr | Total Domination in Rooted Product Graphs |
| title_full_unstemmed | Total Domination in Rooted Product Graphs |
| title_short | Total Domination in Rooted Product Graphs |
| title_sort | total domination in rooted product graphs |
| topic | total domination domination rooted product graph |
| url | https://www.mdpi.com/2073-8994/12/11/1929 |
| work_keys_str_mv | AT abelcabreramartinez totaldominationinrootedproductgraphs AT juanarodriguezvelazquez totaldominationinrootedproductgraphs |