Abstract
Previous work by Lesniak (1975) and recently by Qiao and Zhan (2022) established a sharp lower bound for the number of leaves of a tree as a function of its order and diameter. In this note, we derive a lower bound for the number of leaves as a function of the entire sequence of eccentricities, and provide a complete characterisation of all trees attaining equality. We also obtain a new but simpler proof for the diameter-bound. Furthermore, we establish the analogous result for the maximum with respect to the entire eccentric sequence.