Radio k-Labelings for Cartesian Products of Graphs

Motivated by problems in radio channel assignment, we consider the radio k-labeling of cartesian product of two graphs. The objective is to minimize the span of the radio k-labeling. We provide upper and lower bounds for the k-chromatic number of the cartesian product of two graphs. This result helps to determine upper bounds for k-chromatic numbers of the square mesh and of the hypercube.