Radiatic Dimension of a Graph
K. N. Meera, B. Sooryanarayana · 2012
Let G(V,E) be a simple, finite, connected graph. An injective mapping f : V (G) ! Z + such that for every two distinct vertices u,v 2 V (G), |f(u) f(v)| � diam(G) + 1 d(u,v) is called a radio labeling of G. The radio number of f, denoted by rn(f) is the maximum number assigned to any vertex of G. The radio number of G, is the minimum value of rn(f) taken over all radio labelings f of G. A graph G on n vertices is radio graceful if and only if rn(G) = n. In this paper, we define the radiatic dimension of G to be the smallest positive integer k, such that the sequence of injective functions fi :