Maximal Lanzhou index of trees and unicyclic graphs with prescribed diameter

Peichao Wei, Wuding Jia, Francesco Belardo and Muhuo Liu

Applied Mathematics and Computation, 2025, vol. 488, issue C

Abstract: Given a connected graph G, its Lanzhou index is Lz(G)=∑v∈V(G)d(v)2[n−1−d(v)], where n is the order and d(v) is the degree of v∈G. As usual with topological indices and their meaning in Chemical Graph Theory, we are interested in determining the graphs maximizing or minimizing the considered index. We show that by applying the majorization method, we identify all unified extremal trees with maximum Lanzhou index among the trees of order n and diameter d≥8. Using the same method, we identify the unified extremal unicyclic graphs with maximum Lanzhou index among the unicyclic graphs of order n and diameter d≥9 with n≥3d−8.

Keywords: Lanzhou index; Majorization; Trees; Unicyclic graphs; Extremal graphs (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:488:y:2025:i:c:s0096300324005770

DOI: 10.1016/j.amc.2024.129116

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