Abstract
Let [Formula: see text] be a simple graph with no isolated vertices. A dominating set [Formula: see text] of [Formula: see text] is said to be a cosecure dominating set of [Formula: see text], if for every vertex [Formula: see text] there exists a vertex [Formula: see text] such that [Formula: see text] and [Formula: see text] is a dominating set of [Formula: see text]. The Minimum Cosecure Domination problem is to find a minimum cardinality cosecure dominating set of [Formula: see text]. In this paper, we show that the decision version of the problem is NP-complete for split graphs, undirected path graphs (subclasses of chordal graphs), and circle graphs. We also present a linear-time algorithm to compute the cosecure domination number of cographs (subclass of circle graphs). In addition, we present a few results on the approximation aspects of the problem.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call