Improved Bounds for Radio k-Chromatic Number of Hypercube Qn

A number of graph coloring problems have their roots in a communication problem known as the channel assignment problem. The channel assignment problem is the problem of assigning channels nonnegative integers to the stations in an optimal way such that interference is avoidedas reported by Hale 2005 . Radio k-coloring of a graph is a special type of channel assignment problem. Kchikech et al. 2005 have given a lower and an upper bound for radio k-chromatic number of hypercubeQn, and an improvement of their lower bound was obtained by Kola and Panigrahi 2010 . In this paper, we further improve Kola et al.’s lower bound as well as Kchikeck et al.’s upper bound. Also, our bounds agree for nearly antipodal number of Qn when n ≡ 2 mod 4 .