Arumugam, S.; Kala, R. A note on global domination in graphs. (English) Zbl 1224.05357 Ars Comb. 93, 175-180 (2009). Summary: Let \(G=(V,E)\) be a graph. A subset \(S\) of \(V\) is called a dominating set of \(G\) if every vertex in \(V-S\) is adjacent to at least one vertex in \(S\). A global dominating set is a subset \(S\) of \(V\) which is a dominating set of both \(G\) as well as its complement \(\overline G\). The domination number (global domination number) \(\gamma (\gamma _{g})\) of \(G\) is the minimum cardinality of a dominating set (global dominating set) of \(G\). In this paper, we obtain a characterization of bipartite graphs with \(\gamma _{g}=\gamma +1\). We also characterize unicyclic graphs and bipartite graphs with \(\gamma _g=\alpha _0+1\), where \(\alpha _0\) is the vertex covering number of \(G\). Cited in 3 Documents MSC: 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) Keywords:domination; domination number; global domination number; domsaturation number; global domsaturation number PDFBibTeX XMLCite \textit{S. Arumugam} and \textit{R. Kala}, Ars Comb. 93, 175--180 (2009; Zbl 1224.05357)