The 2-domination number of cylindrical graphs
<|reference_start|>The 2-domination number of cylindrical graphs: A vertex subset S of a graph G is said to 2-dominate the graph if each vertex not in S has at least two neighbors in it. As usual, the associated parameter is the minimum cardinal of a 2-dominating set, which is called the 2-domination number of the graph G. We present both lower and upper bounds of the 2-domination number of cylinders, which are the Cartesian products of a path and a cycle. These bounds allow us to compute the exact value of the 2-domination number of cylinders where the path is arbitrary, and the order of the cycle is n $\equiv$ 0(mod 3) and as large as desired. In the case of the lower bound, we adapt the technique of the wasted domination to this parameter and we use the so-called tropical matrix product to obtain the desired bound. Moreover, we provide a regular patterned construction of a minimum 2-dominating set in the cylinders having the mentioned cycle order.<|reference_end|>
@article{martínez2024the,
    title={The 2-domination number of cylindrical graphs},
    author={Jos'e Antonio Mart'inez, Ana Bel'en Casta~no-Fern'andez and
  Mar'ia Luz Puertas},
    journal={Comp. Appl. Math. 41, 424 (2022)},
    year={2024},
    doi={10.1007/s40314-022-02137-1},
    archivePrefix={arXiv},
    eprint={2409.16703},
    primaryClass={math.CO cs.DM}
}