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.

Keywords:

‎‎Increasing trees‎ , the Wiener index‎ , ‎the Gutman index‎ , ‎degree distance