The extremal graphs of order trees and their topological indices

Rui Song, Qiongxiang Huang and Peng Wang

Applied Mathematics and Computation, 2021, vol. 398, issue C

Abstract: Recently, D. Vukičević and J. Sedlar in [1] introduced an order “⪯” on Tn, the set of trees on n vertices, such that the topological index F of a graph is a function defined on the order set 〈Tn,⪯〉. It provides a new approach to determine the extremal graphs with respect to topological index F. By using the method they determined the common maximum and/or minimum graphs of Tn with respect to topological indices of Wiener type and anti-Wiener type. Motivated by their researches we further study the order set 〈Tn,⪯〉 and give a criterion to determine its order, which enable us to get the common extremal graphs in four prescribed subclasses of 〈Tn,⪯〉. All these extremal graphs are confirmed to be the common maximum and/or minimum graphs with respect to the topological indices of Wiener type and anti-Wiener type. Additionally, we calculate the exact values of Wiener index for the extremal graphs in the order sets 〈C(n,k),⪯〉,〈Tn(q),⪯〉 and 〈TnΔ,⪯〉.

Keywords: Order set; Tree; Extremal graph; Topological index F of a graph (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:398:y:2021:i:c:s0096300321000369

DOI: 10.1016/j.amc.2021.125988

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