The radio number of (Wn: 2) graphs
R. Sweetly, J. Paulraj Joseph · Journal of Discrete Mathematical Sciences and Cryptography · 2009
Let d(u, v) denote the distance between two distinct vertices of a connected graph G, and diam(G) be the diameter of G. A radio labeling c of G is an assignment of positive integers to the vertices of G satisfying d(u, v) + |c(u) — c(v) | ≥ diam(G) + 1. The maximum integer in the range of the labeling is its span. The radio number of G, rn(G), is the minimum possible span. If Wn denote the wheel on n vertices, then the graph obtained from Wn by subdividing each edge of the rim exactly twice is denoted by (Wn : 2). In this paper we prove that the radio number of (Wn : 2) is 5n + 2.