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.

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 South Korean film business has captured the imagination of many young people nowadays, which disturbs many parents. This research seeks to understand the experiences of fandom in young Iranian women from Korean series and its relationship with virtual space. The current qualitative case study research was conducted using thematic analysis and semi-structured interviews, and the data were analyzed using coding. Twenty-three young girls between the ages of 19 and 27 who live in various places in Iran and are members of fan pages on Telegram made up the present research participants.  Although many of them ascribed the start of their fandom to the period when popular Korean series were broadcast on TV, the results of this research confirm that their fandom is sustained thanks to the availability of virtual space. Furthermore, five main themes for the support of these young women were counted from their responses: a variety of genres in products, avoiding erotic scenes, fostering cultural similarities, teaching moral virtue, and attractive romances were among the reasons for their support.

The present study was conducted to identify the motivations of spectators to watch e-sports with quality and meta-combined method (7-step method of Sandlowski and Barso). The statistical population was the researches from 2010 to 2022 in this field, which were collected from valid databases with accurate software. Formal and resource validity has been confirmed by distributing coding sheets among 11 university professors and experts in this field. The Scott coefficient was used for reliability and was confirmed at 85%. Out of 121 initial studies, 18 studies were selected to enter the next stages. In the final stage, all articles were approved in terms of quality control using the Critical Assessment Questionnaire and the consistency of scores. Open, associative and selective coding were also examined from the extraction of component categories. They were divided into three exciting categories. Emotional motivations included sub-components of winning, arousal, being spectacular, surrogate emotions, escape from everyday life, and drama. Cognitive motivation (learning and aesthetics) included knowledge acquisition (of how to play), aesthetics, player skills, attractiveness and innovation, and new. Social status and self-confidence were also components of behavioral motivation.