Predicting graph energy and entropy analysis of pent-heptagonal nanomaterials: Insights from regression models using generalized reverse degree-sum topological indices

Abstract

Nanostructures have sparked notable interest in materials science due to their diverse applications, especially carbon nanosheets with pentagonal–heptagonal variations have emerged as subjects of intense scientific investigation. These nanostructures show great potential in a wide range of fields, including energy storage, optoelectronics, catalysis, and bioelectronics, thereby making substantial contributions to nanotechnology and material science. Topological indices hold a pivotal position in the domain of mathematical and computational chemistry providing numerical information about molecular structures. This information is instrumental in establishing predictive relationships with chemical and physical properties, finding applications across various fields such as drug development and materials science. This paper introduces a novel generalized version of reverse degree-sum based topological indices that effectively shaping the degree sequence of nanomaterials to fit the physical and chemical properties of dataset, differentiating it from conventional fixed-degree methods. Consequently, we explore entropy-based methodologies to compare the structural complexities of pent-heptagonal nanosheets. Furthermore, our study predicts the graph energies of these nanosheets via linear regression equations, comparing them with energy values predicted by the McClelland equation.