Secure domination number of generalized thorn graphs
A secure dominating set S ⊆ V is a dominating set of G satisfying the condition that for each u ∈ V \ S, there exists a vertex v ∈ N(u) ∩ S such that (S \ {v}) S {u} is a dominating set of G. The minimum cardinality of a secure dominating set of G is called the secure domination number of G, γs(G)....
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| Language: | English |
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University of Mohaghegh Ardabili
2025-06-01
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| Series: | Journal of Hyperstructures |
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| Online Access: | https://jhs.uma.ac.ir/article_3843_434c7307f916a24939bef07eb0fb7cf8.pdf |
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| author | Gisha Saraswathy Manju Menon |
| author_facet | Gisha Saraswathy Manju Menon |
| author_sort | Gisha Saraswathy |
| collection | DOAJ |
| description | A secure dominating set S ⊆ V is a dominating set of G satisfying the condition that for each u ∈ V \ S, there exists a vertex v ∈ N(u) ∩ S such that (S \ {v}) S {u} is a dominating set of G. The minimum cardinality of a secure dominating set of G is called the secure domination number of G, γs(G). In this paper, we obtain the secure domination number of generalized thorn paths, thorn graphs, and some special graph classes like thorn rod, thorn star and Kragujevac trees, where the generalized thorn paths are important in the study of chemical compounds. |
| format | Article |
| id | doaj-art-3c60dd4b58814330ae5e2a33c215bb35 |
| institution | OA Journals |
| issn | 2251-8436 2322-1666 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | University of Mohaghegh Ardabili |
| record_format | Article |
| series | Journal of Hyperstructures |
| spelling | doaj-art-3c60dd4b58814330ae5e2a33c215bb352025-08-20T02:36:16ZengUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-84362322-16662025-06-011419310510.22098/jhs.2025.15658.10363843Secure domination number of generalized thorn graphsGisha Saraswathy0Manju Menon1Research Scholar, Dept. of Mathematics, St. Paul's College, Kalamassery, India.Dept. of Mathematics, St. Paul's College, Kalamassery, India.A secure dominating set S ⊆ V is a dominating set of G satisfying the condition that for each u ∈ V \ S, there exists a vertex v ∈ N(u) ∩ S such that (S \ {v}) S {u} is a dominating set of G. The minimum cardinality of a secure dominating set of G is called the secure domination number of G, γs(G). In this paper, we obtain the secure domination number of generalized thorn paths, thorn graphs, and some special graph classes like thorn rod, thorn star and Kragujevac trees, where the generalized thorn paths are important in the study of chemical compounds.https://jhs.uma.ac.ir/article_3843_434c7307f916a24939bef07eb0fb7cf8.pdfsecure domination numberthorn graphsgeneralized thorn pathskragujevac trees |
| spellingShingle | Gisha Saraswathy Manju Menon Secure domination number of generalized thorn graphs Journal of Hyperstructures secure domination number thorn graphs generalized thorn paths kragujevac trees |
| title | Secure domination number of generalized thorn graphs |
| title_full | Secure domination number of generalized thorn graphs |
| title_fullStr | Secure domination number of generalized thorn graphs |
| title_full_unstemmed | Secure domination number of generalized thorn graphs |
| title_short | Secure domination number of generalized thorn graphs |
| title_sort | secure domination number of generalized thorn graphs |
| topic | secure domination number thorn graphs generalized thorn paths kragujevac trees |
| url | https://jhs.uma.ac.ir/article_3843_434c7307f916a24939bef07eb0fb7cf8.pdf |
| work_keys_str_mv | AT gishasaraswathy securedominationnumberofgeneralizedthorngraphs AT manjumenon securedominationnumberofgeneralizedthorngraphs |