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The 2-domination number of cylindrical graphs
- Source :
- Comp. Appl. Math. 41, 424 (2022)
- Publication Year :
- 2024
-
Abstract
- 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.<br />Comment: 19 pages, 4 figures
Details
- Database :
- arXiv
- Journal :
- Comp. Appl. Math. 41, 424 (2022)
- Publication Type :
- Report
- Accession number :
- edsarx.2409.16703
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s40314-022-02137-1