Distance two labeling of direct product of paths and cycles

Suppose that $[n]=\{0,1,2,\mathrm{.}\mathrm{.}\mathrm{.},n\}$ is a set of non-negative integers and $h,k\in [n]$. The $L(h,k)$-labeling of graph $G$ is the function $l:V(G)\to [n]$ such that $\mid l(u)-l(v)\mid \ge h$ if the distance $d(u,v)$ between $u$ and $v$ is one and $\mid l(u)-l(v)\mid \ge k$ if the distance $d(u,v)$ is two. Let $L(V(G))=\{l(v):v\in V(G)\}$ and let $p$ be the maximum value of $L(V(G))\mathrm{.}$ Then $p$ is called ${\lambda }_h^k-$number of $G$ if $p$ is the least possible member of $[n]$ such that $G$ maintains an $L(h,k)-$labeling. In this paper, we establish ${\lambda }_1^1-$ numbers of $P _m \times C_n$graphsforall$m \geq 2$and$n\geq 3$.