Wang, Chunxiang Independence number in claw-free cubic graphs. (Chinese. English summary) Zbl 1199.05272 Acta Math. Sci., Ser. A, Chin. Ed. 29, No. 1, 145-150 (2009). Summary: A set \(X\) is independent if no two vertices of \(X\) are adjacent. A set \(X\) is dominating if \(N[X]=V(G)\). A dominating set \(X\) is minimal if no set \(X\backslash \{x\}\) with \(x\in X\) is dominating. The independence number \(i(G)(\beta(G))\) is the minimum (maximum) cardinality of a maximal independent set of \(G\). The domination number \(\gamma(G)\) (the upper domination number \(\Gamma(G))\) is the minimum (maximum) cardinality of a minimal dominating set of \(G\). In this paper, we prove that: (1)if \(G\in \operatorname{Re}\) and \(G\) is a cubic graph of order \(n\), then \(\gamma(G)=i(G)\), \(\beta(G)=n/3\); (2)for every connected claw-free cubic graph \(G\) of order \(n\), if \(G\) (\(G\neq K_4\)) contains no \(K_4-e\) as induced subgraph, then \(\beta(G)=n/3\). MSC: 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C15 Coloring of graphs and hypergraphs Keywords:cubic graph; domination number; independence number; colouring PDFBibTeX XMLCite \textit{C. Wang}, Acta Math. Sci., Ser. A, Chin. Ed. 29, No. 1, 145--150 (2009; Zbl 1199.05272)