^{1}Science and Research Branch, Islamic Azad University

^{2}Shahid Rajaee Teacher Training University

Abstract

A watching system in a graph $G=(V, E)$ is a set $W=\{\omega_{1}, \omega_{2}, \dots, \omega_{k}\}$, where $\omega_{i}=(v_{i}, Z_{i}), v_{i}\in V$ and $Z_{i}$ is a subset of closed neighborhood of $v_{i}$ such that the sets $L_{W}(v)=\{\omega_{i}: v\in Z_{i}\}$ are non-empty and distinct, for any $v\in V$. In this paper, we study the watching systems of line graph $K_{n}$ which is called triangular graph and denoted by $T(n)$. The minimum size of a watching system of $G$ is denoted by $\omega(G)$. We show that $\omega(T(n))=\lceil\frac{2n}{3}\rceil$.

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