Degree distance and Gutman index of increasing trees

‎‎The Gutman index and degree distance of a connected graph G G are defined as‎ ‎‎‎Gut(G)=∑ {u,v}⊆V(G) d(u)d(v)d G (u,v)‎,‎ ‎‎Gut(G)=∑{u,v}⊆V(G)d(u)d(v)dG(u,v)‎,‎‎ ‎and‎ ‎‎‎DD(G)=∑ {u,v}⊆V(G) (d(u)+d(v))d G (u,v)‎,‎ ‎‎DD(G)=∑{u,v}⊆V(G)(d(u)+d(v))dG(u,v)‎,‎‎ ‎respectively‎, ‎where‎ ‎d(u) d(...

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Main Authors:	Ramin Kazemi, Leila Meimondari
Format:	Article
Language:	English
Published:	University of Isfahan 2016-06-01
Series:	Transactions on Combinatorics
Subjects:	‎‎Increasing trees‎ the Wiener index‎ ‎the Gutman index‎ ‎degree distance
Online Access:	http://www.combinatorics.ir/article_9915_00377372a764b119bb3640a24a194a64.pdf

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author	Ramin Kazemi Leila Meimondari
author_facet	Ramin Kazemi Leila Meimondari
author_sort	Ramin Kazemi
collection	DOAJ
description	‎‎The Gutman index and degree distance of a connected graph G G are defined as‎ ‎‎‎Gut(G)=∑ {u,v}⊆V(G) d(u)d(v)d G (u,v)‎,‎ ‎‎Gut(G)=∑{u,v}⊆V(G)d(u)d(v)dG(u,v)‎,‎‎ ‎and‎ ‎‎‎DD(G)=∑ {u,v}⊆V(G) (d(u)+d(v))d G (u,v)‎,‎ ‎‎DD(G)=∑{u,v}⊆V(G)(d(u)+d(v))dG(u,v)‎,‎‎ ‎respectively‎, ‎where‎ ‎d(u) d(u) is the degree of vertex u u and d G (u,v) dG(u,v) is the distance between vertices u u and v 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.
first_indexed	2024-04-12T06:11:07Z
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institution	Directory Open Access Journal
issn	2251-8657 2251-8665
language	English
last_indexed	2024-04-12T06:11:07Z
publishDate	2016-06-01
publisher	University of Isfahan
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series	Transactions on Combinatorics
spelling	doaj.art-e6e9fad4538e4ccaaa779aed3e9392f52022-12-22T03:44:42ZengUniversity of IsfahanTransactions on Combinatorics2251-86572251-86652016-06-01522331Degree distance and Gutman index of increasing treesRamin Kazemi0Leila Meimondari1Department of statistics, Imam Khomeini International University, QazvinImam Khomeini International University‎‎The Gutman index and degree distance of a connected graph G G are defined as‎ ‎‎‎Gut(G)=∑ {u,v}⊆V(G) d(u)d(v)d G (u,v)‎,‎ ‎‎Gut(G)=∑{u,v}⊆V(G)d(u)d(v)dG(u,v)‎,‎‎ ‎and‎ ‎‎‎DD(G)=∑ {u,v}⊆V(G) (d(u)+d(v))d G (u,v)‎,‎ ‎‎DD(G)=∑{u,v}⊆V(G)(d(u)+d(v))dG(u,v)‎,‎‎ ‎respectively‎, ‎where‎ ‎d(u) d(u) is the degree of vertex u u and d G (u,v) dG(u,v) is the distance between vertices u u and v 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.http://www.combinatorics.ir/article_9915_00377372a764b119bb3640a24a194a64.pdf‎‎Increasing trees‎the Wiener index‎‎the Gutman index‎‎degree distance
spellingShingle	Ramin Kazemi Leila Meimondari Degree distance and Gutman index of increasing trees Transactions on Combinatorics ‎‎Increasing trees‎ the Wiener index‎ ‎the Gutman index‎ ‎degree distance
title	Degree distance and Gutman index of increasing trees
title_full	Degree distance and Gutman index of increasing trees
title_fullStr	Degree distance and Gutman index of increasing trees
title_full_unstemmed	Degree distance and Gutman index of increasing trees
title_short	Degree distance and Gutman index of increasing trees
title_sort	degree distance and gutman index of increasing trees
topic	‎‎Increasing trees‎ the Wiener index‎ ‎the Gutman index‎ ‎degree distance
url	http://www.combinatorics.ir/article_9915_00377372a764b119bb3640a24a194a64.pdf
work_keys_str_mv	AT raminkazemi degreedistanceandgutmanindexofincreasingtrees AT leilameimondari degreedistanceandgutmanindexofincreasingtrees

Degree distance and Gutman index of increasing trees

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