Characterizing minimal point set dominating sets
Purnima V. Gupta, Rajesh Singh, S. Arumugam · AKCE International Journal of Graphs and Combinatorics · 2016
Dedicated to sweet memories of Dr. B.D AcharyaA set of vertices in a graph is said to be a point-set dominating set (or, in short, psd-set) of if for every subset of there exists a vertex such that the subgraph is connected; the set of all psd-sets of will be denoted . The point-set domination number of a graph denoted by is the minimum cardinality of a psd-set of . We obtain a lower bound for and characterize graphs which attain this bound. A psd-set of a graph is minimal if no proper subset of is a psd-set of . In this paper, we give a general characterization of psd-sets which are minimal. Also, in the case of separable graphs, we obtain more transparent and structure specific characterizations of minimal psd-sets.