TY - JOUR
ID - 4127
TI - Watching systems of triangular graphs
JO - Transactions on Combinatorics
JA - TOC
LA - en
SN - 2251-8657
AU - Roozbayani, Maryam
AU - Maimani, Hamidreza
AU - Tehranian, Abolfazl
AD - Science and Research Branch, Islamic Azad University
AD - Shahid Rajaee Teacher Training University
Y1 - 2014
PY - 2014
VL - 3
IS - 1
SP - 51
EP - 57
KW - Identifying code
KW - Watching system
KW - Triangular graph
DO - 10.22108/toc.2014.4127
N2 - 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 $\omega(T(n))=\lceil\frac{2n}{3}\rceil$.
UR - https://toc.ui.ac.ir/article_4127.html
L1 - https://toc.ui.ac.ir/article_4127_d8e4a0adef0fedf9f732d00d5f2d641f.pdf
ER -