فهرست نشریات علمی دسترسی آزاد ایران

‎‎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.