Maximum Wiener Index of Trees With Given Segment Sequence

Authors

Eric Ould Dadah Andriantiana, Stellenbosch UniversityFollow
Stephan G. Wagner, Graz University of Technology
Hua Wang, Georgia Southern UniversityFollow

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