Watching systems of triangular graphs
Maryam Roozbayani, Hamidreza Maimani, Abolfazl Tehranian · DOAJ (DOAJ: Directory of Open Access Journals) · 2014
A watching system in a graph $G=(V, E)$ is a set $W={omega_{1}, omega_{2}, cdots, omega_{k}}$, 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 $L_{W}(v)={omega_{i}: vin omega_{i}}$ are non-empty and distinct, for any $vin V$. 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 $omega(T(n))=lceilfrac{2n}{3}rceil$.