مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Information Journal Paper

Title

On the watching number of graphs

Pages

  179-188

Abstract

 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.

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