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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus


IMPACT FACTOR 2017: 1.414

CiteScore 2018: 1.15

SCImago Journal Rank (SJR) 2018: 0.370
Source Normalized Impact per Paper (SNIP) 2018: 0.431

Online
ISSN
1865-7109
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Volume 61, Issue 10-11

Issues

On Modified and Reverse Wiener Indices of Trees

Bing Zhang / Bo Zhou
Published Online: 2014-06-02 | DOI: https://doi.org/10.1515/zna-2006-10-1104

The Wiener index is a well-known measure of graph or network structures with similarly useful variants of modified and reverse Wiener indices. The Wiener index of a tree T obeys the relation W(T)=nT,1(e)·nT,2(e) where nT,1(e) and nT,2(e) are the number of vertices of T lying on the two sides of the edge e, and where the summation goes over all edges of T. The λ -modified Wiener index is defined as mWλ (T) =[nT,1(e)·nT,2(e)]λ . For each λ > 0 and each integer d with 3 ≤ d ≤ n− 2, we determine the trees with minimal λ -modified Wiener indices in the class of trees with n vertices and diameter d. The reverse Wiener index of a tree T with n vertices is defined as Λ(T)=½n(n-1)d(T)-W(T), where d(T) is the diameter of T. We prove that the reverse Wiener index satisfies the basic requirement for being a branching index.

Keywords : Modified Wiener Index; Reverse Wiener Index; Tree; Diameter

About the article

Received: 2006-08-01

Published Online: 2014-06-02

Published in Print: 2006-11-01


Citation Information: Zeitschrift für Naturforschung A, Volume 61, Issue 10-11, Pages 536–540, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-2006-10-1104.

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© 1946 – 2014: Verlag der Zeitschrift für Naturforschung. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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