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).
Volume 130, 2020
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