on the maximal randić energy of trees with given diameter

For given integers $n,d$ with $ngeq 5$ and $4leq d leq n-1$, let $t^{n}_d$ be the family of all trees of order $n$ and diameter $d$. in this paper, we study trees $tin t^{n}_d$ with maximal randić energy. we prove that if $tin t^{n}_d$ is a tree with maximal randić  energy then $t$ is obtained from a path $p=v_{0}v_{1} ldots v_{d}$ by adding $ n_i$ path(s) $p_{3}$ to each vertex $v_{i}$, for $i= 2,3,4,ldots,d-2$, where $n_iin {lceilfrac{n-d+3}{2d-6}rceil , lfloor frac{n-d+3}{2d-6}rfloor}$. in particular, we present families of trees satisfying the gutman-furtula-bozkurt conjecture proposed in [linear algebra appl., 442 (2014), 50-57].