Radio degree of a graph.

A labeling f : V (G) → Z⁺ such that |f(u) − f(v)|≥diam(G) + 1 − d(u, v) holds for every u, v ∈ V (G), is called a radio labeling of G. We define the radio degree of a labeling f : V (G) → {1, 2, … |V (G)|} as the number of pairs of vertices u, v ∈ V (G) satisfying the condition |f(u) - f(v)|≥diam(G) + 1 - d(u, v) and denote it by rdeg(f). The maximum value of rdeg(f) taken over all such labelings is defined as the radio degree of the graph denoted by rdeg(G). In this paper, we find the radio degree of some standard graphs like paths, cycles, complete graphs, complete bipartite graphs and also obtain a characterization of graphs of diameter two that achieve the maximum radio degree. [ABSTRACT FROM AUTHOR]