Maximum Wiener Index of Trees With Given Segment Sequence

Eric Ould Dadah Andriantiana; Stephan G. Wagner; Hua Wang

Maximum Wiener Index of Trees With Given Segment Sequence

Eric Ould Dadah Andriantiana, Stephan G. Wagner, Hua Wang

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

A segment of a tree is a path whose ends are branching vertices (vertices of degree greater than 2) or leaves, while all other vertices have degree 2. The lengths of all the segments of a tree form its segment sequence. In this note we consider the problem of maximizing the Wiener index among trees with given segment sequence or number of segments, answering two questions proposed in a recent paper on the subject. We show that the maximum is always obtained for a so-called quasi-caterpillar, and we also further characterize its structure.

Original language	American English
Journal	MATCH Communications in Math and Computer Chemistry
Volume	75
State	Published - Jan 1 2016

Keywords

Segment Sequence
Trees
Wiener Index

DC Disciplines

Education
Mathematics

Access to Document

http://math.sun.ac.za/~swagner/segment_sequences.pdf

Cite this

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title = "Maximum Wiener Index of Trees With Given Segment Sequence",

abstract = " A segment of a tree is a path whose ends are branching vertices (vertices of degree greater than 2) or leaves, while all other vertices have degree 2. The lengths of all the segments of a tree form its segment sequence. In this note we consider the problem of maximizing the Wiener index among trees with given segment sequence or number of segments, answering two questions proposed in a recent paper on the subject. We show that the maximum is always obtained for a so-called quasi-caterpillar, and we also further characterize its structure.",

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T1 - Maximum Wiener Index of Trees With Given Segment Sequence

AU - Andriantiana, Eric Ould Dadah

AU - Wagner, Stephan G.

AU - Wang, Hua

PY - 2016/1/1

Y1 - 2016/1/1

N2 - A segment of a tree is a path whose ends are branching vertices (vertices of degree greater than 2) or leaves, while all other vertices have degree 2. The lengths of all the segments of a tree form its segment sequence. In this note we consider the problem of maximizing the Wiener index among trees with given segment sequence or number of segments, answering two questions proposed in a recent paper on the subject. We show that the maximum is always obtained for a so-called quasi-caterpillar, and we also further characterize its structure.

AB - A segment of a tree is a path whose ends are branching vertices (vertices of degree greater than 2) or leaves, while all other vertices have degree 2. The lengths of all the segments of a tree form its segment sequence. In this note we consider the problem of maximizing the Wiener index among trees with given segment sequence or number of segments, answering two questions proposed in a recent paper on the subject. We show that the maximum is always obtained for a so-called quasi-caterpillar, and we also further characterize its structure.

KW - Segment Sequence

KW - Trees

KW - Wiener Index

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/710

UR - http://math.sun.ac.za/~swagner/segment_sequences.pdf

M3 - Article

VL - 75

JO - MATCH Communications in Math and Computer Chemistry

JF - MATCH Communications in Math and Computer Chemistry

ER -

Maximum Wiener Index of Trees With Given Segment Sequence

Abstract

Keywords

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