Vertices Contained In All Or In No Minimum Semitotal Dominating Set Of A Tree
Let G be a graph with no isolated vertex. In this paper, we study a parameter that is squeezed between arguably the two most important domination parameters; namely, the domination number, γ(G), and the total domination number, γt(G). A set S of vertices in a graph G is a semitotal dominating set of...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2016-02-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.1844 |
| _version_ | 1797704369075912704 |
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| author | Henning Michael A. Marcon Alister J. |
| author_facet | Henning Michael A. Marcon Alister J. |
| author_sort | Henning Michael A. |
| collection | DOAJ |
| description | Let G be a graph with no isolated vertex. In this paper, we study a parameter that is squeezed between arguably the two most important domination parameters; namely, the domination number, γ(G), and the total domination number, γt(G). A set S of vertices in a graph G is a semitotal dominating set of G if it is a dominating set of G and every vertex in S is within distance 2 of another vertex of S. The semitotal domination number, γt2(G), is the minimum cardinality of a semitotal dominating set of G. We observe that γ(G) ≤ γt2(G) ≤ γt(G). We characterize the set of vertices that are contained in all, or in no minimum semitotal dominating set of a tree. |
| first_indexed | 2024-03-12T05:19:21Z |
| format | Article |
| id | doaj.art-0ab1ec90410442bc8663b8914b351135 |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T05:19:21Z |
| publishDate | 2016-02-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-0ab1ec90410442bc8663b8914b3511352023-09-03T07:47:23ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922016-02-01361719310.7151/dmgt.1844dmgt.1844Vertices Contained In All Or In No Minimum Semitotal Dominating Set Of A TreeHenning Michael A.0Marcon Alister J.1Department of Pure and Applied Mathematics University of Johannesburg Auckland Park, 2006, South AfricaDepartment of Pure and Applied Mathematics University of Johannesburg Auckland Park, 2006, South AfricaLet G be a graph with no isolated vertex. In this paper, we study a parameter that is squeezed between arguably the two most important domination parameters; namely, the domination number, γ(G), and the total domination number, γt(G). A set S of vertices in a graph G is a semitotal dominating set of G if it is a dominating set of G and every vertex in S is within distance 2 of another vertex of S. The semitotal domination number, γt2(G), is the minimum cardinality of a semitotal dominating set of G. We observe that γ(G) ≤ γt2(G) ≤ γt(G). We characterize the set of vertices that are contained in all, or in no minimum semitotal dominating set of a tree.https://doi.org/10.7151/dmgt.1844dominationsemitotal dominationtrees05c69 |
| spellingShingle | Henning Michael A. Marcon Alister J. Vertices Contained In All Or In No Minimum Semitotal Dominating Set Of A Tree Discussiones Mathematicae Graph Theory domination semitotal domination trees 05c69 |
| title | Vertices Contained In All Or In No Minimum Semitotal Dominating Set Of A Tree |
| title_full | Vertices Contained In All Or In No Minimum Semitotal Dominating Set Of A Tree |
| title_fullStr | Vertices Contained In All Or In No Minimum Semitotal Dominating Set Of A Tree |
| title_full_unstemmed | Vertices Contained In All Or In No Minimum Semitotal Dominating Set Of A Tree |
| title_short | Vertices Contained In All Or In No Minimum Semitotal Dominating Set Of A Tree |
| title_sort | vertices contained in all or in no minimum semitotal dominating set of a tree |
| topic | domination semitotal domination trees 05c69 |
| url | https://doi.org/10.7151/dmgt.1844 |
| work_keys_str_mv | AT henningmichaela verticescontainedinallorinnominimumsemitotaldominatingsetofatree AT marconalisterj verticescontainedinallorinnominimumsemitotaldominatingsetofatree |