The maximum radius of graphs with given order and minimum degree

Let 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 3 2 n − 3 δ + 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 ⌊ 3 2 n δ + 1 ⌋ , the extremal value.