Radio Number for Generalized Petersen Graphs $P(n,2)$

Let
$G$
be a connected graph and
$d(\mu,\omega)$
be the distance between any two vertices of
$G$
. The diameter of
$G$
is denoted by
$diam(G)$
and is equal to
$\max \{d(\mu,\omega); \\ \mu,\omega \in G\}$
. The radio labeling (RL) for the graph
$G$
is an injective function
$\digamma:V(G)\rightarrow N\cup \{0\}$
such that for any pair of vertices
$\mu $
and
$\omega \,\,|\digamma (\mu)-\digamma (\omega)|\geq diam(G)-d(\mu,\omega)+1$
. The span of radio labeling is the largest number in
$\digamma (V)$
. The radio number of
$G$
, denoted by
$rn(G)$
is the minimum span over all radio labeling of
$G$
. In this paper, we determine radio number for the generalized Petersen graphs,
$P(n,2)$
,
$n=4k+2$
. Further the lower bound of radio number for
$P(n,2)$
when
$n=4k$
is determined.