The extremal graphs of order trees and their topological indices
Rui Song, Qiongxiang Huang, Peng Wang

TL;DR
This paper investigates extremal trees with respect to Wiener-type topological indices using a new order relation, identifying extremal graphs and calculating their Wiener indices in specific subclasses.
Contribution
It introduces a criterion to determine the order on trees, enabling the identification of common extremal graphs for various subclasses and indices.
Findings
Identified extremal trees for Wiener and anti-Wiener indices.
Calculated Wiener indices for extremal graphs in specific subclasses.
Established a criterion for ordering trees based on topological indices.
Abstract
Recently, D. Vukievi and J. Sedlar in \cite{Vuki} introduced an order "" on , the set of trees on vertices, such that the topological index of a graph is a function defined on the order set . It provides a new approach to determine the extremal graphs with respect to topological index . By using the method they determined the common maximum and/or minimum graphs of with respect to topological indices of Wiener type and anti-Wiener type. Motivated by their researches we further study the order set and give a criterion to determine its order, which enable us to get the common extremal graphs in four prescribed subclasses of . All these extremal graphs are confirmed to be the common maximum and/or minimum…
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Taxonomy
TopicsGraph theory and applications · Synthesis and Properties of Aromatic Compounds · Computational Drug Discovery Methods
