Degree distance and Gutman index of increasing trees

Document Type : Research Paper

Authors

1 Department of statistics, Imam Khomeini International University, Qazvin

2 Imam Khomeini International University

Abstract

‎‎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

Main Subjects

References

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