The maximum radius of graphs with given order and minimum degree

Let GG be a graph with order nn and minimum degree δ(≥2)δ(≥2). Erdős et al. found an upper bound of the radius rr of GG, 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≥3r≥3, we decrease this bound to ⌊32nδ+1⌋, the extremal value.