Watching system in a graph G is a finite set W = {w1, w2, ..., wk}where each wiis a couple wi = (vi, Zi), where viis a vertex andZi ⊆ NG[vi] such that {Z1, ..., Zk} is an identifying system.Theconcept of Watching system was first introduced by Auger in[1]. and this system provide an extension of identifying codein the sense that an identifying code is a particular Watchingsystem. In this paper, we determine the Watching system ofspecific graphs.

The ever-expanding, diverse and rapid growth of change in various fields, it has intensified the impact of threats and opportunities. The world is drastically renewing itself. Adapting to these new conditions requires to preliminary knowledge symptoms of environmental change, readiness to explore new opportunities, avoid newly emerged threats and avoid surprise. One way of informing key officials and decision makers, especially the armed forces, is to use future studies and Watching system. The ultimate goal of Watching is to prevent the surprise of the officials and senior managers of the organization in carrying out their assigned missions. This article introduces the Armed Forces Watching system at strategic levels. In this research, we have used exploratory mix methods (quantitative & qualitative) to achieve the objectives of the research. In the qualitative section, based on a careful study of existing external and internal documents and content analysis and in-depth interviews with 12 experts, elements and processes of the system were extracted. In the next step, the average ranking of the elements and processes of the Armed Forces Watching system at strategic levels and their importance are determined by Friedman test and with the opinions of 31 experienced experts. Cronbach's alpha and combined reliability of the research are 0. 796 and0. 798 respectively. In the research findings, the system elements are ranked from the point of view of experts in three processes of scanning and monitoring strategic documents, Early warning and Knowing the adversary strategic intents of enemies and competitors.

A Watching system in a graph G=(V, E) is a set W={w1, w2, …,wk}, where wi=(vi, Zi); viÎ V and Zi is a subset of closed neighborhood of vi such that the sets LW(v) ={wi: vÎZi} are non-empty and distinct, for any v ÎV. In this paper, we study the Watching systems of line graph Kn which is called triangular graph and denoted by T (n). The minimum size of a Watching system of G is denoted by w (G). We show that w (T(n))= [2n/3].

Let $G=(V‎, ‎E)$ be a simple and undirected graph‎. ‎A watcher $\omega_i$ of $G$ is a couple of $\omega_i=(v_i‎, ‎Z_i),$ where $v_i \in V$ and $Z_i$ is a subset of the closed neighborhood of $v_i.$ If a vertex $v \in Z_i,$ we say that $v$ is covered by $\omega_i.$ A set $W=\{\omega_1‎, ‎\omega_2‎, ‎\dots‎, ‎\omega_k\}$‎, ‎of watchers is a Watching system for $G$ if the sets $L_W(v)=\{\omega_i~:~v \in Z_i‎ ~,~ ‎1 \le i \le k\}$ are non-empty and distinct‎, ‎for every $v \in V$‎. ‎In this paper‎, ‎we study the Watching systems of some graphs‎, ‎and consider the Watching number of Mycielski's construction of some graphs‎.