On the harmonic index in cactus graphs-Reference-Cited by-同舟云学术

On the harmonic index in cactus graphs

Published:2024-02-28 Issue: Volume: Page:
ISSN:1793-8309
Container-title:Discrete Mathematics, Algorithms and Applications
language:en
Short-container-title:Discrete Math. Algorithm. Appl.

Author:

Rad Nader Jafari¹^ORCID,Hasni Roslan²^ORCID,Kamarulhaili Hailiza³^ORCID

Affiliation:

1. Department of Mathematics, Shahed University, Tehran, Iran

2. Special Interest Group on Modeling and Data Analytics (SIGMDA), Faculty of Computer Science and Mathematics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia

3. School of Mathematical Science, Universiti Sains Malaysia, 11800 USM Penang, Malaysia

Abstract

The harmonic index of graph [Formula: see text] is the value [Formula: see text], where [Formula: see text] refers to the degree of [Formula: see text]. Zhong [The harmonic index for graphs, Appl. Math. Lett. 25 (2012) 561–566] proved that [Formula: see text] for any tree [Formula: see text] of order [Formula: see text]. As a results of Ali, Raza and Bhatti [Some vertex-degree-based topological indices of cacti, Ars Combin. 144 (2019) 195–206], it can be shown that [Formula: see text] for any tree [Formula: see text] of order [Formula: see text] with [Formula: see text] leaves, where [Formula: see text]. In this paper, we generalize this lower bound for all cactus graphs. We present a lower bound for the harmonic index of cactus graphs [Formula: see text] in terms of the order, the number of leaves and the number of cycles, and characterize all cactus graphs achieving equality for the given bound.

Publisher

World Scientific Pub Co Pte Ltd

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793830924500113