Unveiling strong domination number on some graphs
Slashi Leel2022301198.slashi@dr.sharda.ac.inDepartment of MathematicsSharda UniversityGreater Noida, Uttar Pradesh, 201310, IndiaView full profile → , Sweta Srivastavsweta.srivastav@sharda.ac.inDepartment of MathematicsSharda UniversityGreater Noida, Uttar Pradesh, 201310, IndiaView full profile → , *Sangeeta GuptaCorresponding authorsangeeta.gupta@sharda.ac.inDepartment of MathematicsSharda UniversityGreater Noida, Uttar Pradesh, 201310, IndiaView full profile →
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- Received:
- 01 Dec 2025
- Published Online:
- 30 Sep 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2855
- Pages:
- 3409–3418
Abstract
Let G = (V, E) be the given graph, a subset D ⊆ V is defined as the dominating set if every vertices in the set (V-D) is adjacent to at least one vertex in the set D. Then the set D is known as the Dominating set. Let xy ∈ E be an edge in Graph G then x strongly dominates y if deg x ≥ deg y. Set D is known as a strong dominating set of G if every vertex of (V-D) is strongly dominated by some element in set D. Strong domination number is the minimum cardinality of strong dominating set it is represented by γst(G). In this paper we investigated the strong domination number of crown graph, sunflower graph, vertex switching of gear graph, vertex switching of wheel graph. Applications of strong domination numbers extend to security frameworks and alert-based systems, emphasizing their importance in net- work reliability and control.
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References
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