  A radio labeling of a graph $G$ is a function $f : V(G) \rightarrow
\{0,1,2,\ldots\}$ such that $|f(u)-f(v)| \geq diam(G) + 1 - d(u,v)$ for every
pair of distinct vertices $u,v$ of $G$. The radio number of $G$, denoted by
$rn(G)$, is the smallest number $k$ such that $G$ has radio labeling $f$ with
max$\{f(v):v \in V(G)\} = k$. In this paper, we give a lower bound for the
radio number for the Cartesian product of the generalized Petersen graph and
tree. We present two necessary and sufficient conditions, and three other
sufficient conditions to achieve the lower bound. Using these results, we
determine the radio number for the Cartesian product of the Peterson graph and
stars.
