Strong equality of domination parameters in trees
Let \(\gamma(G)\) denote the domination number of graph \(G\), i.e., the minimum cardinality of a dominating vertex set in \(G\), let \(i(G)\) denote the independent domination number of \(G\), i.e., the minimum cardinality of an independent dominating vertex set in \(G\), let \(\gamma_t(G)\) denote the total domination number of graph \(G\), i.e., the minimum cardinality of a totally dominating vertex set in \(G\) (here, the vertices in the dominating set must dominate each other), and let \(\gamma_p(G)\) denote the paired-domination number of graph \(G\), i.e., the minimum cardinality of a dominating vertex set \(S\) in \(G\) such that \(G[S]\) contains at least one perfect matching. This paper gives a constructive characterization of the trees \(T\) for which, first, \(\gamma(T)= i(T)\), second, \(\gamma(T)= \gamma_t(T)\), and third, \(\gamma(T)= \gamma_p(T)\).
scientific article; zbMATH DE number 1882180