RADIO LABELING AND RADIO NUMBER FOR GENERALIZED CATERPILLAR GRAPHS
Saima Nazeer, Muhammad Khan, Imrana Kousar, Waqas Nazeer · Journal of applied mathematics & informatics · 2016
A Radio labeling of the graph G is a function g from the vertex set V (G) of G to ℤ+ such that |g(u) - g(v)| ≥ diam(G) + 1 - dG(u, v), where diam(G) and d(u, v) are diameter and distance between u and v in graph G respectively. The radio number rn(G) of G is the smallest number k such that G has radio labeling with max{g(v) : v ∈ V(G)} = k. We investigate radio number for some families of generalized caterpillar graphs.