The relation between the number of leaves of a tree and its diameter

Let L(n, d) denote the minimum possible number of leaves in a tree order n and diameter d. Lesniak (1975) gave lower bound B(n,d) = ⌈2(n − 1)/d⌉ for L(n,d). When d is even, But when odd, smaller than L(n,d) general. For example, B(21, 3) 14 while L(21, 19. In this note, we determine using new ideas. We also consider converse problem with given leaves.