Domination number on an octagonal chain and an octagonal grid

UDC 519.1 Domination of the graph and topological indices are essential topics in the graph theory. We analyze the problem of $k$-domination, $k\in\{1,2,3\}$, on octagonal chains and an octagonal grid. We determine the minimal $k$-dominating sets and $k$-domination $k$ numbers for a chain of octagons with two common vertices. By using the obtained results, we determine the $k$-domination numbers for the grid of octagons $O_{mxn}$ with $m,n\in N$.