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Comparative analysis of planar octahedron molecular structure via Zagreb connection indices

School of Mathematical Sciences, Anhui University, Hefei, People’s Republic of China

Received: 15 July 2025 Accepted: 19 October 2025

Abstract:

Abstract

In the field of chemical engineering, we utilize a mathematical parameter known as a topological index to characterize the shape and connectivity of molecules. We conduct calculations based on the structure of molecules, which also enables us to predict their physical and chemical properties. Ultimately, the complex relationship between molecular structure and these calculations highlights the essential role that geometry plays in forecasting the physical and chemical properties of substances. These properties can encompass aspects such as biological activity, solubility, and reactivity. The primary objective of this research is to calculate the Zagreb connection indices for a planar octahedron network. This network serves as a model for numerous coordination chemicals and molecular complexes. The covalent or ionic connections formed between the core atom and its surrounding counterparts contribute to the stability and integrity of the network. This structure is important in the field of coordination chemistry. Metal centers usually choose the planar octahedral network as their coordination environment. Transition-metal complexes typically adopt octahedral geometries, which are three-dimensional and have a great effect on their magnetic and spectroscopic properties. In the present work, we calculate the first, second and first modified Zagreb connection indices for an n-dimensional planar octahedron structure. In addition, we compute the hyper-Zagreb connection index, harmonic connection index, augmented Zagreb connection index, geometric-arithmetic connection index, and atom-bond connectivity connection index. Graphical analysis is also provided at the end before the conclusion.

Graphical abstract

Keywords: Planar octahedron network; Zagreb connection indices; Molecular topology; Comparability; Quantum chemical design

Full paper is available at www.springerlink.com.

DOI: 10.1007/s11696-025-04468-9

Chemical Papers 80 (2) 1521–1533 (2026)

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