Zhou, Ligang; Shan, Erfang; Wang, Haichao Total dominating functions on subclasses of chordal graphs. (Chinese. English summary) Zbl 1240.05238 OR Trans. 14, No. 1, 85-94 (2010). Summary: In this paper, we show that the \(k\)-total domination and the signed total domination problems are NP-complete on doubly chordal graphs. Also, we present an unified approach to solve the signed total domination, minus total domination, \(k\)-total domination and \(\{k\}\)-total domination problems on a strongly chordal graph in linear-time, if the strong elimination ordering for the strongly chordal graph is given. MSC: 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C22 Signed and weighted graphs 05C85 Graph algorithms (graph-theoretic aspects) Keywords:total dominating function; signed total domination; minus total domination; strongly chordal graphs; doubly chordal graphs PDFBibTeX XMLCite \textit{L. Zhou} et al., OR Trans. 14, No. 1, 85--94 (2010; Zbl 1240.05238)