Some Results on the Strong Roman Domination Number of Graphs
Let G=(V,E) be a finite and simple graph of order n and maximum degree Δ(G). A strong Roman dominating function on a graph G is a function f:V (G)→{0, 1,… ,[Δ(G)/2 ]+ 1} satisfying the condition that every vertex v for which f(v)=0 is adjacent to at least one vertex u for which...
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| Format: | Article |
| Language: | English |
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University of Kashan
2020-09-01
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| Series: | Mathematics Interdisciplinary Research |
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| Online Access: | https://mir.kashanu.ac.ir/article_110816_2ff1aa058881fe3c1ad101ed2efb2b99.pdf |
| _version_ | 1827765031579680768 |
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| author | Akram Mahmoodi Sakineh Nazari-Moghaddam Afshin Behmaram |
| author_facet | Akram Mahmoodi Sakineh Nazari-Moghaddam Afshin Behmaram |
| author_sort | Akram Mahmoodi |
| collection | DOAJ |
| description | Let G=(V,E) be a finite and simple graph of order n and maximum degree Δ(G). A strong Roman dominating function on a graph G is a function f:V (G)→{0, 1,… ,[Δ(G)/2 ]+ 1} satisfying the condition that every vertex v for which f(v)=0 is adjacent to at least one vertex u for which f(u) ≤ 1+ [(1/2)| N(u) ∩ V0| ], where V0={v ∊ V | f(v)=0}. The minimum of the values ∑v∊ V f(v), taken over all strong Roman dominating functions f of G, is called the strong Roman domination number of G and is denoted by γStR(G). In this paper we continue the study of strong Roman domination number in graphs. In particular, we present some sharp bounds for γStR(G) and we determine the strong Roman domination number of some graphs. |
| first_indexed | 2024-03-11T11:13:19Z |
| format | Article |
| id | doaj.art-48db3b307647419baa3db5a6116166d9 |
| institution | Directory Open Access Journal |
| issn | 2476-4965 |
| language | English |
| last_indexed | 2024-03-11T11:13:19Z |
| publishDate | 2020-09-01 |
| publisher | University of Kashan |
| record_format | Article |
| series | Mathematics Interdisciplinary Research |
| spelling | doaj.art-48db3b307647419baa3db5a6116166d92023-11-11T08:14:05ZengUniversity of KashanMathematics Interdisciplinary Research2476-49652020-09-015325927710.22052/mir.2020.225635.1205110816Some Results on the Strong Roman Domination Number of GraphsAkram Mahmoodi0Sakineh Nazari-Moghaddam1Afshin Behmaram2Department of Mathematics, Payame Noor University, I. R. IranDepartment of Mathematics, Dehloran Branch, University of Applied Science and Technology Dehloran, I. R. IranFaculty of Mathematical Sciences, University of Tabriz, Tabriz, I. R. IranLet G=(V,E) be a finite and simple graph of order n and maximum degree Δ(G). A strong Roman dominating function on a graph G is a function f:V (G)→{0, 1,… ,[Δ(G)/2 ]+ 1} satisfying the condition that every vertex v for which f(v)=0 is adjacent to at least one vertex u for which f(u) ≤ 1+ [(1/2)| N(u) ∩ V0| ], where V0={v ∊ V | f(v)=0}. The minimum of the values ∑v∊ V f(v), taken over all strong Roman dominating functions f of G, is called the strong Roman domination number of G and is denoted by γStR(G). In this paper we continue the study of strong Roman domination number in graphs. In particular, we present some sharp bounds for γStR(G) and we determine the strong Roman domination number of some graphs.https://mir.kashanu.ac.ir/article_110816_2ff1aa058881fe3c1ad101ed2efb2b99.pdfdominationroman dominationroman domination numberstrong roman domination |
| spellingShingle | Akram Mahmoodi Sakineh Nazari-Moghaddam Afshin Behmaram Some Results on the Strong Roman Domination Number of Graphs Mathematics Interdisciplinary Research domination roman domination roman domination number strong roman domination |
| title | Some Results on the Strong Roman Domination Number of Graphs |
| title_full | Some Results on the Strong Roman Domination Number of Graphs |
| title_fullStr | Some Results on the Strong Roman Domination Number of Graphs |
| title_full_unstemmed | Some Results on the Strong Roman Domination Number of Graphs |
| title_short | Some Results on the Strong Roman Domination Number of Graphs |
| title_sort | some results on the strong roman domination number of graphs |
| topic | domination roman domination roman domination number strong roman domination |
| url | https://mir.kashanu.ac.ir/article_110816_2ff1aa058881fe3c1ad101ed2efb2b99.pdf |
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