New Bounds on the Triple Roman Domination Number of Graphs
In this paper, we derive sharp upper and lower bounds on the sum γ3RG+γ3RG¯ and product γ3RGγ3RG¯, where G¯ is the complement of graph G. We also show that for each tree T of order n≥2, γ3RT≤3n+sT/2 and γ3RT≥⌈4nT+2−ℓT/3⌉, where sT and ℓT are the number of support vertices and leaves of T....
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/9992618 |
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| author | M. Hajjari H. Abdollahzadeh Ahangar R. Khoeilar Z. Shao S. M. Sheikholeslami |
| author_facet | M. Hajjari H. Abdollahzadeh Ahangar R. Khoeilar Z. Shao S. M. Sheikholeslami |
| author_sort | M. Hajjari |
| collection | DOAJ |
| description | In this paper, we derive sharp upper and lower bounds on the sum γ3RG+γ3RG¯ and product γ3RGγ3RG¯, where G¯ is the complement of graph G. We also show that for each tree T of order n≥2, γ3RT≤3n+sT/2 and γ3RT≥⌈4nT+2−ℓT/3⌉, where sT and ℓT are the number of support vertices and leaves of T. |
| format | Article |
| id | doaj-art-f14fdd14c3c644aabcb5e873a29e18dd |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-f14fdd14c3c644aabcb5e873a29e18dd2025-02-03T06:41:59ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/9992618New Bounds on the Triple Roman Domination Number of GraphsM. Hajjari0H. Abdollahzadeh Ahangar1R. Khoeilar2Z. Shao3S. M. Sheikholeslami4Department of MathematicsDepartment of MathematicsDepartment of MathematicsInstitute of Computing Science and TechnologyDepartment of MathematicsIn this paper, we derive sharp upper and lower bounds on the sum γ3RG+γ3RG¯ and product γ3RGγ3RG¯, where G¯ is the complement of graph G. We also show that for each tree T of order n≥2, γ3RT≤3n+sT/2 and γ3RT≥⌈4nT+2−ℓT/3⌉, where sT and ℓT are the number of support vertices and leaves of T.http://dx.doi.org/10.1155/2022/9992618 |
| spellingShingle | M. Hajjari H. Abdollahzadeh Ahangar R. Khoeilar Z. Shao S. M. Sheikholeslami New Bounds on the Triple Roman Domination Number of Graphs Journal of Mathematics |
| title | New Bounds on the Triple Roman Domination Number of Graphs |
| title_full | New Bounds on the Triple Roman Domination Number of Graphs |
| title_fullStr | New Bounds on the Triple Roman Domination Number of Graphs |
| title_full_unstemmed | New Bounds on the Triple Roman Domination Number of Graphs |
| title_short | New Bounds on the Triple Roman Domination Number of Graphs |
| title_sort | new bounds on the triple roman domination number of graphs |
| url | http://dx.doi.org/10.1155/2022/9992618 |
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