degree distance and gutman index of increasing trees

‎the gutman index and degree distance of a connected graph $g$ are defined as‎ ‎begin{eqnarray*}‎ ‎textrm{gut}(g)=sum_{{u,v}subseteq v(g)}d(u)d(v)d_g(u,v)‎, ‎end{eqnarray*}‎ ‎and‎ ‎begin{eqnarray*}‎ ‎dd(g)=sum_{{u,v}subseteq v(g)}(d(u)+d(v))d_g(u,v)‎, ‎end{eqnarray*}‎ ‎respectively‎, ‎where‎ ‎$d(u)$ is the degree of vertex $u$ and $d_g(u,v)$ is the distance between vertices $u$ and $v$‎. ‎in this paper‎, ‎through a recurrence equation for the wiener index‎, ‎we study the first two‎ ‎moments of the gutman index and degree distance of increasing‎ ‎trees‎.