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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Main Authors: Gisha Saraswathy, Manju Menon
Format: Article
Language:English
Published: University of Mohaghegh Ardabili 2025-06-01
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.
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publisher University of Mohaghegh Ardabili
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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