Radio Secure number of a Graph

Let G(V,E)G(V,E) be a simple, finite, connected graph on n vertices. Let f:V(G)→{1,2………n}f:V(G)→{1,2………n} be an injective mapping. Then the largest cardinality of a set S⊆V(G)S⊆V(G) such that for every pair of distinct vertices u,v∈S,|f(u)−f(v)≥diam(G)+1−d(u,v)u,v∈S,|f(u)−f(v)≥diam(G)+1−d(u,v) is called the radio secure number of f denoted by rs(f)rs(f). The set S is called a radio secure set. The radio secure number of a graph G   is defined as maximum value of rs(f)rs(f) over all such functions f   and is denoted by rs(G)rs(G). It is obvious that 1≤rs(G)≤n1≤rs(G)≤n. If rs(G)=nrs(G)=n, then G is a radio graceful graph. In this paper, we investigate the radio secure number of certain standard graphs like complete graphs, complete bipartite graphs, wheels, paths and cycles.