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 .