Abstract
A set \(S \subseteq V(G)\) is said to be secure if the security condition, for every \(X \subseteq S\), \(\left| N[X] \cap S\right| \ge \left| N[X] - S\right| \) holds. Now, a set \(S \subseteq V(G)\) 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.
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Acknowledgements
The authors thank the referees for their valuable suggestions. The authors thank their teacher Professor A. Vijayakumar, Emiritus Professor, Department of Mathematics, Cochin University of Science and Technology for his suggestions for the improvement of the content in this paper.
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Communicated by Shariefuddin Pirzada.
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Menon, M.K., Chithra, M.R. Secure domination of some graph operators. Indian J Pure Appl Math 54, 1170–1176 (2023). https://doi.org/10.1007/s13226-022-00331-9
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DOI: https://doi.org/10.1007/s13226-022-00331-9