Computational modeling of triangular γ-graphyne using advanced topological methods

Modeling and computation of molecular descriptors play a crucial role in understanding the properties and characteristics of novel materials like [Formula: see text]-graphyne, the next-generation wonder material. Triangular [Formula: see text]-graphyne is an intriguing two-dimensional carbon-based material with diverse potential applications due to its unique electronic, mechanical, and thermal properties. Triangular [Formula: see text]-graphyne, a distinctive form of carbon allotrope, has garnered substantial interest as a result of its extraordinary characteristics. The notable value lies in its ability to be utilized in diverse domains for potential applications. The interconnected mesh structure of Triangular [Formula: see text]-graphyne exhibits exceptional mechanical strength and exceptional electron-transporting properties. This makes it a promising material for the development of high-performance electronic devices, such as transistors and sensors. Furthermore, gamma graphyne possesses excellent thermal stability, which makes it suitable for applications in the field of energy storage and conversion. It has the potential to be used as a catalyst in fuel cells or as an electrode material in supercapacitors. In this study, we utilize graph theory to dissect the molecular structure of triangular [Formula: see text]-graphyne, leading to the derivation of specific mathematical formulas for essential degree-based molecular characteristics. These findings can be instrumental in examining the correlations between the structure and properties of [Formula: see text]-graphyne. This paper focuses on two structures made from hexagonal honeycomb graphite lattices, like triangular [Formula: see text]-graphyne and triangular [Formula: see text]-graphyne chains with respect to some degree-based topological indices. The results obtained will aid in the investigation of the structure-property relationships in [Formula: see text]-graphyne.