Extremal caterpillar-like trees relative to the Wiener index - Dingile, Ndimphiwe Bradley Morné (Rhodes University, 2026)
The Wiener index of a graph \(G\) is the sum of the distances between all vertex pairs in \(G\). A caterpillar-like tree is a tree where all its branching vertices (vertices of degree at least 3) lie on the same path. This project focuses on the class of caterpillar-like trees with given order and other restrictions such as number of leaves and maximum degree. The aim is to determine the structures of those caterpillar-like trees that reach the minimum (and maximum) Wiener index under the prescribed restrictions.
Keywords: Graph theory (http://id.loc.gov/authorities/subjects/sh85056471); Mathematics; Wiener index (https://www.wikidata.org/wiki/Q909065); Caterpillar tree (https://www.wikidata.org/wiki/Q5051951)