Raczek, Joanna Graphs with equal domination and 2-distance domination numbers. (English) Zbl 1234.05179 Discuss. Math., Graph Theory 31, No. 2, 375-385 (2011). Summary: Let \(G= (V,F)\) be a graph. The distance between two vertices \(u\) and \(v\) in a connected graph \(G\) is the length of the shortest \((u-v)\) path in \(G\). A set \(D\subseteq V(G)\) is a dominating set if every vertex of \(G\) is at distance at most 1 from an element of \(D\). The domination number of \(G\) is the minimum cardinality of a dominating set of \(G\). A set \(D\subseteq V(G)\) is a 2-distance dominating set if every vertex of \(G\) is at distance at most 2 from an element of \(D\). The 2-distance domination number of \(G\) is the minimum cardinality of a 2-distance dominating set of \(G\). We characterize all trees and all unicyclic graphs with equal domination and 2-distance domination numbers. Cited in 1 Document MSC: 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C12 Distance in graphs 05C05 Trees Keywords:distance domination number; trees; unicyclic graphs PDFBibTeX XMLCite \textit{J. Raczek}, Discuss. Math., Graph Theory 31, No. 2, 375--385 (2011; Zbl 1234.05179) Full Text: DOI Link