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 radio number of path graphs and cycle graphs
were determined by Liu and Zhu (2005). The following table
summarizes some known results for a number of special families of graphs.