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Topological indices serve as mathematical tools for characterising the molecular structure of a compound, and are useful to anticipate its properties. Actually, these are quantitative measures that can provide valuable information regarding the structure of a molecule, such as its connectivity and symmetry. By analysing these indices, researchers can make predictions about the behaviour of the molecule, such as its reactivity, solubility, and toxicity, among others. The γ-Graphyne is a fascinating carbon allotrope that has recently gained significant attention due to its unique electronic, optical, and mechanical properties. As a result, there has been increasing interest in exploring its potential applications in various fields of science and technology. The molecular descriptors for the characterisation of γ-Graphyne have not yet been investigated. Therefore, it is of much importance to predict its molecular topology to well understand the physicochemical properties. In this work, a graph theory-based edge partitioning technique is used to model the molecular topology of γ-Graphyne and Zigzag graphyne nanoribbon, and mathematical closed-form expressions for some of its essential degree-based molecular descriptors are derived. These computed indices have been illustrated with the help of graphical representations and numerical tables.

Computation of some important degree-based topological indices for γ- graphyne and Zigzag graphyne nanoribbon