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Secure domination of some graph operators

Manju K. Menon () and M. R. Chithra ()
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Manju K. Menon: St. Paul’s College
M. R. Chithra: University of Kerala

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 4, 1170-1176

Abstract: Abstract A set $$S \subseteq V(G)$$ S ⊆ V ( G ) is said to be secure if the security condition, for every $$X \subseteq S$$ X ⊆ S , $$\left| N[X] \cap S\right| \ge \left| N[X] - S\right| $$ N [ X ] ∩ S ≥ N [ X ] - S holds. Now, a set $$S \subseteq V(G)$$ S ⊆ V ( G ) is secure dominating if it is both secure and dominating. The secure domination number of G is the minimum cardinality of a secure dominating set in G. In this paper, we have obtained results regarding the secure domination number of some graph operators.

Keywords: Secure set; Secure domination number; Generalized Mycielskian; Double graph; Corona; 05C69; 05C76 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00331-9

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