Harmonic-Arithmetic Index of Unicyclic Graphs

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Ding Guoqing; Zhong Lingping; Wang Xia

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Journal Paper

Paper Information

Journal: Iranian Journal of Mathematical Chemistry Year:2025 | Volume:16 | Issue:2 Page(s): 93-108

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Information Journal Paper

Title

Harmonic-Arithmetic Index of Unicyclic Graphs

Author(s)

Ding Guoqing | Zhong Lingping | Wang Xia | Issue Writer Certificate

Keywords

Harmonic-arithmetic index

Extremal graph

unicyclic graph

Abstract

‎Let G=(V(G), E(G)) be a graph‎. ‎The Harmonic-arithmetic index of G is defined as $HA(G)=\sum_{uv\in E(G)}\frac{4d_{G}(u)d_{G}(v)}{(d_{G}(u)+d_{G}(v))^2}$‎, ‎where $d_{G}(u)$ is the degree of a vertex $u\in V(G)$‎. ‎In this paper‎, ‎we consider the upper and lower bounds of the Harmonic-arithmetic index of unicyclic graphs with a fixed order‎. ‎Furthermore‎, ‎the graphs attaining the extremal values are also characterised.

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