Degree distance and Gutman index of increasing trees

Kazemi, Ramin; Meimondari, Leila

doi:10.22108/toc.2016.9915

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	Degree distance and Gutman index of increasing trees
Transactions on Combinatorics
مقاله 3، دوره 5، شماره 2، شهریور 2016، صفحه 23-31 اصل مقاله (290.67 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2016.9915
نویسندگان
Ramin Kazemi^* ¹؛ Leila Meimondari²
¹Department of statistics, Imam Khomeini International University, Qazvin
²Imam Khomeini International University
چکیده
‎‎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.
کلیدواژه‌ها
‎‎Increasing trees‎؛ the Wiener index‎؛ ‎the Gutman index‎؛ ‎degree distance

مراجع
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Degree distance and Gutman index of increasing trees