No abstract

The radio k-coloring is an assignment l of non-negative integers to the vertices of a graph in such a way that for two vertices u, v which are d distance apart, we must haveThe difference between the greatest and the least image of l is its span and our objective is to minimize the span. That is, the radio k-chromatic number rc k (G) is the minimum λ such that it is a span of some radio k-coloring of G. In this article, we find exact values of rc k (P m n ) when k > diam(P m n ) + ǫ, where P m n denotes the m th power of a path on (n + 1) vertices, and diam(P m n ) denotes its diameter.