Further results on independent double roman trees
AbstractA double Roman dominating function (DRDF) on a graph [Formula: see text] is a function [Formula: see text] such that every vertex u with f(u) = 0 is adjacent to at least one vertex assigned a 3 or to at least two vertices assigned a 2, and every vertex v with f(v) = 1 is adjacent to at least...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2022-09-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2022.2148140 |
| _version_ | 1811209356738297856 |
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| author | A. Rahmouni H. Abdollahzadeh Ahangar M. Chellali S. M. Sheikholeslami |
| author_facet | A. Rahmouni H. Abdollahzadeh Ahangar M. Chellali S. M. Sheikholeslami |
| author_sort | A. Rahmouni |
| collection | DOAJ |
| description | AbstractA double Roman dominating function (DRDF) on a graph [Formula: see text] is a function [Formula: see text] such that every vertex u with f(u) = 0 is adjacent to at least one vertex assigned a 3 or to at least two vertices assigned a 2, and every vertex v with f(v) = 1 is adjacent to at least one vertex assigned 2 or 3. The weight of a DRDF is the sum of its function values over all vertices. A DRDF f is an independent double Roman dominating function (IDRDF) if the set of vertices assigned 1, 2 and 3 is independent. The independent double Roman domination number [Formula: see text] is the minimum weight over all IDRDFs of G. Every graph G satisfies [Formula: see text] where i(G) is the independent domination number. In this paper, we give a characterization of all trees T with [Formula: see text] |
| first_indexed | 2024-04-12T04:38:03Z |
| format | Article |
| id | doaj.art-89565dedd2174940823bcda06dea7350 |
| institution | Directory Open Access Journal |
| issn | 0972-8600 2543-3474 |
| language | English |
| last_indexed | 2024-04-12T04:38:03Z |
| publishDate | 2022-09-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj.art-89565dedd2174940823bcda06dea73502022-12-22T03:47:44ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742022-09-0119331131510.1080/09728600.2022.2148140Further results on independent double roman treesA. Rahmouni0H. Abdollahzadeh Ahangar1M. Chellali2S. M. Sheikholeslami3LAMDA-RO Laboratory, Department of Mathematics, University of Blida, Blida, AlgeriaDepartment of Mathematics, Babol Noshirvani University of Technology, Babol, I.R. IranLAMDA-RO Laboratory, Department of Mathematics, University of Blida, Blida, AlgeriaDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz, IranAbstractA double Roman dominating function (DRDF) on a graph [Formula: see text] is a function [Formula: see text] such that every vertex u with f(u) = 0 is adjacent to at least one vertex assigned a 3 or to at least two vertices assigned a 2, and every vertex v with f(v) = 1 is adjacent to at least one vertex assigned 2 or 3. The weight of a DRDF is the sum of its function values over all vertices. A DRDF f is an independent double Roman dominating function (IDRDF) if the set of vertices assigned 1, 2 and 3 is independent. The independent double Roman domination number [Formula: see text] is the minimum weight over all IDRDFs of G. Every graph G satisfies [Formula: see text] where i(G) is the independent domination number. In this paper, we give a characterization of all trees T with [Formula: see text]https://www.tandfonline.com/doi/10.1080/09728600.2022.2148140Independent double Roman dominationindependent dominationtrees05C6905C05 |
| spellingShingle | A. Rahmouni H. Abdollahzadeh Ahangar M. Chellali S. M. Sheikholeslami Further results on independent double roman trees AKCE International Journal of Graphs and Combinatorics Independent double Roman domination independent domination trees 05C69 05C05 |
| title | Further results on independent double roman trees |
| title_full | Further results on independent double roman trees |
| title_fullStr | Further results on independent double roman trees |
| title_full_unstemmed | Further results on independent double roman trees |
| title_short | Further results on independent double roman trees |
| title_sort | further results on independent double roman trees |
| topic | Independent double Roman domination independent domination trees 05C69 05C05 |
| url | https://www.tandfonline.com/doi/10.1080/09728600.2022.2148140 |
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