Let 
be a finite, connected, undirected
graph with graph diameter 
and graph distance 
between vertices 
and 
. A radio labeling of a graph 
is labeling using distinct nonnegative
integers such that 
for every pair of distinct vertices 
, 
in the vertex set of 
. Then the radio number of 
, commonly denoted 
, is the smallest integer 
such that 
has a radio labeling 
with 
.
The smallest integer 
such that 
has a radio labeling 
with 
is known as the radio number of 
, commonly denoted 
.
Define 
.
A radio labeling 
of 
is optimal if 
.
