Michaël Rao ; Alexandre Talon - The 2-domination and Roman domination numbers of grid graphs

dmtcs:4952 - Discrete Mathematics & Theoretical Computer Science, May 23, 2019, vol. 21 no. 1, ICGT 2018 - https://doi.org/10.23638/DMTCS-21-1-9
The 2-domination and Roman domination numbers of grid graphsArticle

Authors: Michaël Rao ; Alexandre Talon

    We investigate the 2-domination number for grid graphs, that is the size of a smallest set $D$ of vertices of the grid such that each vertex of the grid belongs to $D$ or has at least two neighbours in $D$. We give a closed formula giving the 2-domination number of any $n \!\times\! m$ grid, hereby confirming the results found by Lu and Xu, and Shaheen et al. for $n \leq 4$ and slightly correct the value of Shaheen et al. for $n = 5$. The proof relies on some dynamic programming algorithms, using transfer matrices in (min,+)-algebra. We also apply the method to solve the Roman domination problem on grid graphs.

    Volume: vol. 21 no. 1, ICGT 2018
    Published on: May 23, 2019
    Accepted on: May 3, 2019
    Submitted on: November 2, 2018
    Keywords: Computer Science - Discrete Mathematics,Mathematics - Combinatorics

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