Locating and paired-dominating sets in graphs
In this paper, we continue the study of paired-domination in graphs introduced by Haynes and Slater [T.W. Haynes, P.J. Slater, Paired-domination in graphs, Networks 32 (1998), 199206]. A paired-dominating set of a graph G G with no isolated vertex is a dominating set S S of vertices whose induced subgraph has a perfect matching. We consider paired-dominating sets which are also locating sets, that is distinct vertices of G G are dominated by distinct subsets of the paired-dominating set. We consider three variations of sets which are paired-dominating and locating sets and investigate their properties.
differentiating-paired-dominating set locating-paired-dominating set metric-locating-paired-dominating set