Abdul Hakeem ^1* Nek Muhammad Katbar ^1,2 Hisamuddin Shaikh ³ Fikadu Tolasa ⁴ Oshaque Abro ⁵

• ¹ Central South University, Changsha, China
• ² School of Mathematics and Statistics, Central South University, Changsha, Hunan Province, China
• ³ Department of Geography, Shah Abdul Latif University, Khairpur, Sindh, Pakistan
• ⁴ Dambi Dollo University, Dambi Dollo, Ethiopia
• ⁵ Dawood University of Engineering and Technology, Karachi, Sindh, Pakistan

Topological indices are mathematical descriptors of the structure of a molecule that can be used to predict its properties. They are derived from the graph theory, which describes the topology of a molecule and its connectivity. The main objective is mathematical modeling and topological properties of ϒgraphyne. Current research focuses on two structures made from hexagonal honeycomb graphite lattices named triangular ϒgraphyne and triangular ϒgraphyne chains. The authors have simultaneously computed the first and second Reverse Zagreb indices, reverse hyper-Zagreb indices, and their polynomials. This research also derives mathematical closed-form formulas for some of its fundamental degree-based molecular descriptors. Researchers have been trying to synthesize a novel carbon form called Graphyne. For over a decade but with no success. Recently, some researchers have made a breakthrough in generating Carbons elusive allotrope and solved a long-standing problem in carbon materials. This wonder material is created to rival the conductivity of graphene but with control. These results opened new ways of research in the fields of semiconductors, electronics and optics. Furthermore, graphical and tabular results will help to investigate the structure-property relationships in γ-graphyne.