motivated by the terminal wiener index, we define the ashwini index $mathcal{a}$ of trees as begin{eqnarray*} % nonumber to remove numbering (before each equation) mathcal{a}(t) &=& sumlimits_{1leq i&+& deg_{_{t}}(n(v_{j}))], end{eqnarray*} where $d_{t}(v_{i}, v_{j})$ is the distance between the vertices $v_{i}, v_{j} in v(t)$, is equal to the length of the shortest path start...