Interconnections among Radio Number, Clique Number and Chromatic Number

Let \(G(V,Ε)\) be a simple, connected and undirected graph. A radio labeling of G, \(ψ:V→{1,2,3,…} \) is a function satisfying the condition for any two distinct vertices u and v that: \(d(u,v)+|ψ(u)-ψ(v)|≥1+diam(G), \) where d(u, v) denotes the distance between the vertices u and v and diam(G) denotes the diameter of the graph G. The of a radio labeling is the maximum integer that assigns to a vertex and radio number, rn(G) is the minimum span taken overall radio labelings of G. This paper presents some bounds connecting radio number with clique number and the chromatic number. In addition, the possible constructions of simple connected graphs with radio number as the algebraic sum of clique number and a non-negative integer. Also, graph with radio number equal to the algebraic sum of chromatic number and a non-negative integer.