Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 11 4 2026 12 01 On 4-domination and 4-rainbow domination of cylindrical graphs 1125 1140 15063 10.22049/cco.2025.30780.2616 EN Janez Žerovnik FME, University of Ljubljana, Aškerčeva 6, Ljubljana, 1000, Slovenia Rudolfovo - Science and Technology Centre Novo Mesto, Podbreznik 15, Novo mesto, 8000, Slovenia Journal Article 2025 07 09 Cylindrical graphs and torus grid graphs are naturally constructed from sub-graphs of the infinite grid by certain identifications of boundary vertices. Considering various domination type problems, it is usually possible to find an optimal solution on the infinite grid. To the contrary, exact values of invariants for the cylindrical and torus grid graphs are typically only known for special subfamilies, and are in general hard to compute. The 4-domination and 4-rainbow domination of cylindrical graphs is studied, and some new formulae and improved bounds are reported, generalizing recent results for the case $k = 2$ in [Computational and Applied Mathematics 44(5), 293 (2025)]. We also consider weak 4-domination and singleton 4-rainbow domination. https://comb-opt.azaruniv.ac.ir/article_15063_298f446d63ac403ca9ba7b34cf485d68.pdf