Brewster, Richard C.; MacGillivray, Gary Minimizing \(\beta+\Delta\) and well covered graphs. (English) Zbl 1071.05054 Ars Comb. 61, 197-210 (2001). Let \(\beta , \gamma , \Delta \) be the independence number, the domination number and the maximum degree of a vertex of a graph \(G\). Let \(n\) be the number of vertices of \(G\). The inequality \(\gamma + \Delta \geq \lceil 2 \sqrt n - 1 \rceil \) is proved and the graphs attaining this minimum are studied. Further the attention is focused onto a stronger condition \(\beta + \Delta = \lceil 2 \sqrt n - 1 \rceil \). Reviewer: Bohdan Zelinka (Liberec) MSC: 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) Keywords:independence number; domination number; maximum degree of a graph PDFBibTeX XMLCite \textit{R. C. Brewster} and \textit{G. MacGillivray}, Ars Comb. 61, 197--210 (2001; Zbl 1071.05054)