• The exact 2-domination number of generalized Petersen graphs

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/130/0054

• # Keywords

2-Domination number; generalized Petersen graph.

• # 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).

• # Author Affiliations

1. Department of Mathematics, North China Electric Power University, Beijing 102206, China

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019