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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Roozbayani, M., Maimani, H., & Tehranian, A. (2014). Watching systems of triangular graphs. Transactions on Combinatorics, 3(1), 51-57. doi: 10.22108/toc.2014.4127
MLA
Maryam Roozbayani; Hamidreza Maimani; Abolfazl Tehranian. "Watching systems of triangular graphs". Transactions on Combinatorics, 3, 1, 2014, 51-57. doi: 10.22108/toc.2014.4127
HARVARD
Roozbayani, M., Maimani, H., Tehranian, A. (2014). 'Watching systems of triangular graphs', Transactions on Combinatorics, 3(1), pp. 51-57. doi: 10.22108/toc.2014.4127
VANCOUVER
Roozbayani, M., Maimani, H., Tehranian, A. Watching systems of triangular graphs. Transactions on Combinatorics, 2014; 3(1): 51-57. doi: 10.22108/toc.2014.4127
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