The domination number of \(C_8 \times C_n\) and \(C_9 \times C_n\). (English) Zbl 0935.05070

Summary: A set \(D\) of vertices of a simple graph \(G= (V,E)\) is called dominating if every vertex \(v\in V-D\) is adjacent to some vertex \(\mu\in D\). The domination number of a graph \(G\), \(\Gamma(G)\), is the order of a smallest dominating set of \(G\). We calculate the domination numbers of the toroidal grid graphs \(C_8\times C_n\) and \(C_9\times C_n\). The domination numbers of \(C_m\times C_n\), for \(m= 5\) and \(n\equiv 3\pmod 5\), and also for \(m= 6, 7\) and arbitrary \(n\) were calculated by the authors in a previous paper.


05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)