Abstract
Identifying code in graph [Formula: see text] is a subset [Formula: see text] of [Formula: see text] such that [Formula: see text] for every [Formula: see text] of [Formula: see text] and [Formula: see text] for every [Formula: see text] of [Formula: see text]. The minimum size of identifying codes of graph [Formula: see text] is denoted by [Formula: see text]. A watching system in a graph [Formula: see text] is a set [Formula: see text], where [Formula: see text] and [Formula: see text] is a subset of closed neighborhood of [Formula: see text] such that the sets [Formula: see text] are nonempty and distinct, for any [Formula: see text]. The minimum size of a watching system of [Formula: see text] is denoted by [Formula: see text]. In this paper, we show if [Formula: see text], then [Formula: see text] if [Formula: see text] (mod 3) and [Formula: see text] if [Formula: see text] (mod 3). Also we show that [Formula: see text]. This means that in this family of graphs the watching system is more efficient than identifying code.
Sign-in/Register to access full text options 
Free) 
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
