New Bounds on the Signed Total Domination Number of Graphs
In this paper, we study the signed total domination number in graphs and present new sharp lower and upper bounds for this parameter. For example by making use of the classic theorem of Turán [8], we present a sharp lower bound on Kr+1-free graphs for r ≥ 2. Applying the concept of total limited pac...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Zielona Góra
2016-05-01
|
| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.1871 |
| _version_ | 1797757762352971776 |
|---|---|
| author | Moghaddam Seyyed Mehdi Hosseini Mojdeh Doost Ali Samadi Babak Volkmann Lutz |
| author_facet | Moghaddam Seyyed Mehdi Hosseini Mojdeh Doost Ali Samadi Babak Volkmann Lutz |
| author_sort | Moghaddam Seyyed Mehdi Hosseini |
| collection | DOAJ |
| description | In this paper, we study the signed total domination number in graphs and present new sharp lower and upper bounds for this parameter. For example by making use of the classic theorem of Turán [8], we present a sharp lower bound on Kr+1-free graphs for r ≥ 2. Applying the concept of total limited packing we bound the signed total domination number of G with δ(G) ≥ 3 from above by . Also, we prove that γst(T) ≤ n − 2(s − s′) for any tree T of order n, with s support vertices and s′ support vertices of degree two. Moreover, we characterize all trees attaining this bound. |
| first_indexed | 2024-03-12T18:20:09Z |
| format | Article |
| id | doaj.art-6b7258078b234ac8afc415931131bc29 |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T18:20:09Z |
| publishDate | 2016-05-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-6b7258078b234ac8afc415931131bc292023-08-02T08:58:46ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922016-05-0136246747710.7151/dmgt.1871dmgt.1871New Bounds on the Signed Total Domination Number of GraphsMoghaddam Seyyed Mehdi Hosseini0Mojdeh Doost Ali1Samadi Babak2Volkmann Lutz3Sama Technical and Vocatinal Training CollegeIslamic Azad University, Qom Branch, Qom, IranDepartment of Mathematics, University of Mazandaran, Babolsar, IranDepartment of Mathematics, Arak University, Arak, IranLehrstuhl II für Mathematik RWTH Aachen University, 52056 Aachen, GermanyIn this paper, we study the signed total domination number in graphs and present new sharp lower and upper bounds for this parameter. For example by making use of the classic theorem of Turán [8], we present a sharp lower bound on Kr+1-free graphs for r ≥ 2. Applying the concept of total limited packing we bound the signed total domination number of G with δ(G) ≥ 3 from above by . Also, we prove that γst(T) ≤ n − 2(s − s′) for any tree T of order n, with s support vertices and s′ support vertices of degree two. Moreover, we characterize all trees attaining this bound.https://doi.org/10.7151/dmgt.1871open packingsigned total domination numbertotal limited packingtuple total domination number |
| spellingShingle | Moghaddam Seyyed Mehdi Hosseini Mojdeh Doost Ali Samadi Babak Volkmann Lutz New Bounds on the Signed Total Domination Number of Graphs Discussiones Mathematicae Graph Theory open packing signed total domination number total limited packing tuple total domination number |
| title | New Bounds on the Signed Total Domination Number of Graphs |
| title_full | New Bounds on the Signed Total Domination Number of Graphs |
| title_fullStr | New Bounds on the Signed Total Domination Number of Graphs |
| title_full_unstemmed | New Bounds on the Signed Total Domination Number of Graphs |
| title_short | New Bounds on the Signed Total Domination Number of Graphs |
| title_sort | new bounds on the signed total domination number of graphs |
| topic | open packing signed total domination number total limited packing tuple total domination number |
| url | https://doi.org/10.7151/dmgt.1871 |
| work_keys_str_mv | AT moghaddamseyyedmehdihosseini newboundsonthesignedtotaldominationnumberofgraphs AT mojdehdoostali newboundsonthesignedtotaldominationnumberofgraphs AT samadibabak newboundsonthesignedtotaldominationnumberofgraphs AT volkmannlutz newboundsonthesignedtotaldominationnumberofgraphs |