Geodesic
The 2-domination and Roman domination numbers of grid graphs
Discrete mathematics & theoretical computer science, ICGT 2018, Tome 21 (2019) no. 1.

Voir la notice de l'article provenant de la source Episciences

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. 
@article{DMTCS_2019_21_1_a5,
     author = {Rao, Micha\"el and Talon, Alexandre},
     title = {The 2-domination and {Roman} domination numbers of grid graphs},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2019},
     doi = {10.23638/DMTCS-21-1-9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-1-9/}
}
TY  - JOUR
AU  - Rao, Michaël
AU  - Talon, Alexandre
TI  - The 2-domination and Roman domination numbers of grid graphs
JO  - Discrete mathematics & theoretical computer science
PY  - 2019
VL  - 21
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-1-9/
DO  - 10.23638/DMTCS-21-1-9
LA  - en
ID  - DMTCS_2019_21_1_a5
ER  - 
%0 Journal Article
%A Rao, Michaël
%A Talon, Alexandre
%T The 2-domination and Roman domination numbers of grid graphs
%J Discrete mathematics & theoretical computer science
%D 2019
%V 21
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-1-9/
%R 10.23638/DMTCS-21-1-9
%G en
%F DMTCS_2019_21_1_a5
Rao, Michaël; Talon, Alexandre. The 2-domination and Roman domination numbers of grid graphs. Discrete mathematics & theoretical computer science, ICGT 2018, Tome 21 (2019) no. 1. doi : 10.23638/DMTCS-21-1-9. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-1-9/

Cité par Sources :