An
L
h
,
k
-labeling of a graph
G
=
V
,
E
is a function
f
:
V
⟶
0
,
∞
such that the positive difference between labels of the neighbouring vertices is at least
h
and the positive difference between the vertices separated by a distance 2 is at least
k
. The difference between the highest and lowest assigned values is the index of an
L
h
,
k
-labeling. The minimum number for which the graph admits an
L
h
,
k
-labeling is called the required possible index of
L
h
,
k
-labeling of
G
, and it is denoted by
λ
k
h
G
. In this paper, we obtain an upper bound for the index of the
L
h
,
k
-labeling for an inverse graph associated with a finite cyclic group, and we also establish the fact that the upper bound is sharp. Finally, we investigate a relation between
L
h
,
k
-labeling with radio labeling of an inverse graph associated with a finite cyclic group.
Radio labeling to the transformation of cycle
