The maximum radius of graphs with given order and minimum degree

AbstractLet G be a graph with order n and minimum degree δ(≥2). Erdős et al. found an upper bound of the radius r of G, which is 32n−3δ+1+5. They noted that this bound is tight apart from the exact value of the additive constant. In this paper, when r≥3, we decrease this bound to ⌊32nδ+1⌋, the extremal value