Radio Antipodal Number of Certain Graphs

Let G = (V, E) be a graph with vertex set V and edge set E. Let diam(G) denote the diameter of G and d(u, v) denote the distance between the vertices it and v in G. An antipodal labeling of G with diameter d is a function f that assigns to each vertex u, a positive integer f(u), such that d(u, v) + If (u) f (v)I >= d, for all u, v e v. The span of an antipodal labeling f is max {vertical bar f (u) - f (v)vertical bar: u,v is an element of V(G)}. The antipodal number for G, denoted by an(G), is the minimum span of all antipodal labelings of G. Determining the antipodal number of a graph G is an NP-complete problem. In this paper we determine the antipodal number of certain graphs.