On the watching number of graphs using discharging procedure

The identifying code has been used to place objects in the sensor and wireless networks. For the vertex x of a graph G, suppose $$N_G[x]$$ is a subset of V(G) containing x and all of its neighbors. Then $$C\subseteq V(G)$$ is called an identifying code of G, if for two distinct vertices x and y of G, both $$C\cap N_G[x]$$ and $$C\cap N_G[y]$$ are nonempty and distinct. The watching system of a graph G has been proposed as an extension of identifying code. In this paper, we study some properties of watching system and then, by using a discharging method, we compute the watching of generalized Petersen graph P(n, k) (for $$k=2,3,n/2$$ ) which is commonly used in interconnection networks.