The Radio Antipodal and Radio Numbers of the Hypercube

A radio k-labeling of a connected graph G is an assignment f of non negative integers to the vertices of G such that |f(x)− f(y)| ≥ k + 1− d(x, y), for any two vertices x and y, where d(x, y) is the distance between x and y in G. The radio antipodal number is the minimum span of a radio (diam(G) − 1)-labeling of G and the radio number is the minimum span of a radio (diam(G))-labeling of G. In this paper, the radio antipodal number and the radio number of the hypercube are determined by using a generalization of binary Gray codes.