#### Title

Maximum Wiener Index of Trees With Given Segment Sequence

#### Document Type

Article

#### Publication Date

2016

#### Publication Title

MATCH Communications in Math and Computer Chemistry

#### ISSN

0340-6253

#### 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.

#### Recommended Citation

Andriantiana, Eric Ould Dadah, Stephan G. Wagner, Hua Wang.
2016.
"Maximum Wiener Index of Trees With Given Segment Sequence."
*MATCH Communications in Math and Computer Chemistry*, 75 (1): 1-9.
source: http://match.pmf.kg.ac.rs/electronic_versions/Match75/n1/match75n1_91-104.pdf

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