Domination Number and Secure Resolving Sets in Cyclic Networks

Consider a robot that is navigating graph-based space and attempting to determine where it right now. To how distant from each group of fixed landmarks, can send signal. We discuss the problem determining minimum number landmarks necessary their optimal placement ensure always locate itself. The referred as graph's metric dimension, set nodes on which they are distributed known basis. On other hand, dimension graph G size w vertices identify vertex pair G by shortest-path distance particular in w. It an NP-complete for any network. also used variety applications, including geographic routing protocols, network discovery verification, pattern recognition, image processing, combinatorial optimization. In this paper, we investigate exact value secure resolving some networks, such trapezoid network, Z-(Pn) open ladder tortoise domination twig Tm, double fan F2,n, bistar Bn,n and linear kc4 – snake