Given two non-negative integers $h$ and $k$, the $L(h,k)$-edge labeling of the graph $G=(V(G),E(G))$ is the function is $f. ‘:E(G) \xrightarrow{}\{0,1,\cdots, n\}$ such that $\forall e_1,e_2 \in E(G)$, $\vert f'(e_1)-f ‘ (e_2) \vert \geq h$ then $d'(e_1,e_2)=1$ and $\vert f'(e_1)-f'(e_2) \vert \geq k$ then $d'( e_1,e_2) )=2$ where $d'(e_1,e_2)$ represents the distance between $e_1$ and $e_2$ in $G$. where $d'(e_1,e_2)=k ‘$. The goal is to be the smallest $n$ of all such $L(h,k)edge labeling, with a \textit{span} denoted as $\lambda’_{h,k}(G)$ to find out. Motivated by the channel assignment problem in wireless cellular networks, the $L(h,k)$-edge labeling problem has been studied on various infinite regular grids. $25 \leq \lambda’_{1,2}(T_8) \leq 28$ for infinite regular octagonal lattice $T_8$ [Tiziana Calamoneri,
International Journal of Foundations of Computer Science, Vol. 26, No. 04,
2015] There is a gap between the lower and upper bounds. In this paper, we fill in the gaps and prove that $\lambda’_{1,2}(T_8)= 28$.
