Kazeem Olalekan Aremu ^1,2* Tumiso Kekana ¹ Maggie Aphane ¹

• ¹ Sefako Makgatho Health Sciences University, Pretoria, South Africa
• ² Usmanu Danfodiyo University, Sokoto, Sokoto, Nigeria

Graphene, composed of a single layer of carbon atoms arranged in a hexagonal lattice pattern, has been the focus of extensive research due to its remarkable properties and practical applications. Topological indices (TIs) play a crucial role in studying graphene's structure as mathematical functions mapping molecular graphs to real numbers, capturing their topological characteristics. To compute these TIs, we employ the M-polynomial approach, an efficient method for deriving degree-based descriptors of molecular graphs. In this study, we analyze the neighborhood multiple M-polynomial of graphene's structure and use it to derive eleven neighborhood multiple degree-based TIs. These TIs allow us to predict various properties of graphene theoretically, bypassing the need for experiments or computer simulations. Furthermore, we showcase various numerical and graphical representations emphasizing the intricate connections between TIs and structural parameters. These computations were further employed to analyze the Quantitative Structure-Property Relationship (QSPR) between TIs and the mechanical properties of graphene, such as Young's Modulus, Poisson's Ratio, Shear Modulus, and Tensile Strength. The results showed strong correlations between neighborhood multiple TIs and Poisson's Ratio and Shear Modulus, underscoring their predictive power for these mechanical properties. These findings highlight the effectiveness of neighborhood multiple degree-based TIs in characterizing and predicting the mechanical properties of graphene structures, providing valuable insights for future applications in material science.