More results on the signed double Roman domination number of graphs
A signed double Roman dominating function (SDRD-function) on a graph G is defined as a function [Formula: see text] having the property that [Formula: see text] for each [Formula: see text] and if [Formula: see text], then the vertex u must have a neighbor w with [Formula: see text] or two neighbors...
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| Language: | English |
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Taylor & Francis Group
2025-06-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2025.2511651 |
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| author | Seyed Mahmoud Sheikholeslami Lutz Volkmann |
| author_facet | Seyed Mahmoud Sheikholeslami Lutz Volkmann |
| author_sort | Seyed Mahmoud Sheikholeslami |
| collection | DOAJ |
| description | A signed double Roman dominating function (SDRD-function) on a graph G is defined as a function [Formula: see text] having the property that [Formula: see text] for each [Formula: see text] and if [Formula: see text], then the vertex u must have a neighbor w with [Formula: see text] or two neighbors assigned 2 under f, and if [Formula: see text], then v must have at least one neighbor w with [Formula: see text]. The weight of an SDRD-function f is the value [Formula: see text]. The signed double Roman domination number[Formula: see text] is the minimum weight of an SDRD-function. It is conjectured that the signed double Roman domination number of a nontrivial graph G is bounded above by its order. In this paper we prove this conjecture for cactus graphs, and we present some new bounds on [Formula: see text]. We also determine the signed double Roman domination number of perfect binary trees. |
| format | Article |
| id | doaj-art-49aeed979f4c4a2bbcb8c97d8d4a662c |
| institution | DOAJ |
| issn | 0972-8600 2543-3474 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj-art-49aeed979f4c4a2bbcb8c97d8d4a662c2025-08-20T03:10:58ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742025-06-0112410.1080/09728600.2025.2511651More results on the signed double Roman domination number of graphsSeyed Mahmoud Sheikholeslami0Lutz Volkmann1Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. IranRWTH Aachen University, Aachen, GermanyA signed double Roman dominating function (SDRD-function) on a graph G is defined as a function [Formula: see text] having the property that [Formula: see text] for each [Formula: see text] and if [Formula: see text], then the vertex u must have a neighbor w with [Formula: see text] or two neighbors assigned 2 under f, and if [Formula: see text], then v must have at least one neighbor w with [Formula: see text]. The weight of an SDRD-function f is the value [Formula: see text]. The signed double Roman domination number[Formula: see text] is the minimum weight of an SDRD-function. It is conjectured that the signed double Roman domination number of a nontrivial graph G is bounded above by its order. In this paper we prove this conjecture for cactus graphs, and we present some new bounds on [Formula: see text]. We also determine the signed double Roman domination number of perfect binary trees.https://www.tandfonline.com/doi/10.1080/09728600.2025.2511651Roman dominationsigned double Roman dominationtrees05C69 |
| spellingShingle | Seyed Mahmoud Sheikholeslami Lutz Volkmann More results on the signed double Roman domination number of graphs AKCE International Journal of Graphs and Combinatorics Roman domination signed double Roman domination trees 05C69 |
| title | More results on the signed double Roman domination number of graphs |
| title_full | More results on the signed double Roman domination number of graphs |
| title_fullStr | More results on the signed double Roman domination number of graphs |
| title_full_unstemmed | More results on the signed double Roman domination number of graphs |
| title_short | More results on the signed double Roman domination number of graphs |
| title_sort | more results on the signed double roman domination number of graphs |
| topic | Roman domination signed double Roman domination trees 05C69 |
| url | https://www.tandfonline.com/doi/10.1080/09728600.2025.2511651 |
| work_keys_str_mv | AT seyedmahmoudsheikholeslami moreresultsonthesigneddoubleromandominationnumberofgraphs AT lutzvolkmann moreresultsonthesigneddoubleromandominationnumberofgraphs |