Radio number for strong product $P_2 \otimes P_n$

Abstract

A radio labeling of a graph $G$ is a function $f$ from the vertex set $V(G)$ to the set of non-negative integers such that $|f(u)-f(v)| \geq \operatorname{diam}(G)+1-d_G(u, v)$, where $\operatorname{diam}(G)$ and $d_G(u, v)$ are diameter and distance between $u$ and $v$ in graph $G$ respectively. The radio number $\operatorname{rn}(G)$ of $G$ is the smallest number $k$ such that $G$ has radio labeling with $\max \{f(v): v \in V(G)\}=k$. We investigate radio number for strong product of $P_2$ and $P_n$.