A characterization of trees with equal 2-domination and 2-independence numbers

@article{Brause2017ACO,
  title={A characterization of trees with equal 2-domination and 2-independence numbers},
  author={Christoph Brause and Michael A. Henning and Marcin Krzywkowski},
  journal={Discret. Math. Theor. Comput. Sci.},
  year={2017},
  volume={19}
}
A set $S$ of vertices in a graph $G$ is a $2$-dominating set if every vertex of $G$ not in $S$ is adjacent to at least two vertices in $S$, and $S$ is a $2$-independent set if every vertex in $S$ is adjacent to at most one vertex of $S$. The $2$-domination number $\gamma_2(G)$ is the minimum cardinality of a $2$-dominating set in $G$, and the $2$-independence number $\alpha_2(G)$ is the maximum cardinality of a $2$-independent set in $G$. Chellali and Meddah [{\it Trees with equal $2… 

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