On Harmonic Index and Diameter of Quasi-Tree Graphs

A. Abdolghafourian, Mohammad A. Iranmanesh and Ismail Naci Cangul

Journal of Mathematics, 2021, vol. 2021, 1-9

Abstract: The harmonic index of a graph G (HG) is defined as the sum of the weights 2/du+dv for all edges uv of G, where du is the degree of a vertex u in G. In this paper, we show that HG≥DG+5/3−n/2 and HG≥1/2+2/3n−2DG, where G is a quasi-tree graph of order n and diameter DG. Indeed, we show that both lower bounds are tight and identify all quasi-tree graphs reaching these two lower bounds.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6650407

DOI: 10.1155/2021/6650407

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