No abstract

Let G be a simple connected graph. For any two vertices u and v, let d(u, v) denote the distance between u and v in G. A radio-k-labeling of G for a fixed positive integer k is a function f which assigns to each vertex a non-negative integer label such that for every two vertices u and v in G,The span of f is the difference between the largest and smallest labels of f (V ). The radio-k-number of a graph G, denoted by rn k (G), is the smallest span among all radio-k-labelings admitted by G. A cycle Cn has diameter d = n/2 . In this paper, we combine a lower bound approach with algebraic cyclic group structure to determine the value of rn k (Cn) for k n − 3. For d k < n − 3, we obtain the values of rn k (Cn) when n and k have the same parity, and prove partial results when n and k have different parities. Our results extend the known values of rn d (Cn) and rn d+1 (Cn) shown by Liu and Zhu [14], and by Karst, Langowitz, Oehrlein and Troxell [9], respectively.