E. M. Garzón ; J. A. Martínez ; J. J. Moreno ; M. L. Puertas - On the $2$-domination number of cylinders with small cycles

fi:8516 - Fundamenta Informaticae, May 6, 2022, Volume 185, Issue 2
On the $2$-domination number of cylinders with small cyclesArticle

Authors: E. M. Garzón ; J. A. Martínez ; J. J. Moreno ; M. L. Puertas

    Domination-type parameters are difficult to manage in Cartesian product graphs and there is usually no general relationship between the parameter in both factors and in the product graph. This is the situation of the domination number, the Roman domination number or the $2$-domination number, among others. Contrary to what happens with the domination number and the Roman domination number, the $2$-domination number remains unknown in cylinders, that is, the Cartesian product of a cycle and a path and in this paper, we will compute this parameter in the cylinders with small cycles. We will develop two algorithms involving the $(\min,+)$ matrix product that will allow us to compute the desired values of $\gamma_2(C_n\Box P_m)$, with $3\leq n\leq 15$ and $m\geq 2$. We will also pose a conjecture about the general formulae for the $2$-domination number in this graph class.

    Volume: Volume 185, Issue 2
    Published on: May 6, 2022
    Accepted on: February 10, 2022
    Submitted on: September 23, 2021
    Keywords: Computer Science - Discrete Mathematics,Mathematics - Combinatorics,G.2.2,F.2.2

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