Abstract
Let \(G=(V,E)\) be a graph. A subset \(S\subseteq V\) is a 2-dominating set of G if each vertex in \(V-S\) is adjacent to at least two vertices in S. The 2-domination number of G is the cardinality of the smallest 2-dominating set of G. In this paper, we shall prove that the 2-domination number of generalized Petersen graphs \(P(5k+1,3)\), \(P(5k+2,3)\) and \(P(5k+3,3)\) is \(4k+2\), \(4k+3\) and \(4k+4\), respectively. This proves one conjecture due to Bakhshesh et al. (Proc. Indian Acad. Sci. (Math. Sci.) 128 (2018) 17).
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References
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The authors thank the anonymous reviewers for their valuable comments.
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Communicating Editor: Sukanta Pati
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Chen, Xg., Zhao, Xs. The exact 2-domination number of generalized Petersen graphs. Proc Math Sci 130, 54 (2020). https://doi.org/10.1007/s12044-020-00571-x
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DOI: https://doi.org/10.1007/s12044-020-00571-x