On the watching number of graphs
نویسندگان
1 Department of pure Mathematics, Faculty of science, Imam Khomeini International University, P.O.Box 34149-16818, Qazvin, Iran.
2 Department of pure Mathematics, Faculty of science, Imam Khomeini International University, P.O.Box 34149-16818, Qazvin, Iran.
doi
10.30504/jims.2023.388523.1097چکیده
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.
