Comparative analysis of modified reverse degree topological indices for certain carbon nanosheets using entropy measures and multi criteria decision‐making analysis

Abstract

The diverse applications of various carbon nanostructures have sparked significant research interest. The potential significance of carbon nanosheets lies in their exceptional mechanical, electrical, and thermal properties, enabling advancements in various technological applications such as energy storage, electronics, and engineering, playing important roles in material science and nanotechnology. In the field of mathematical chemistry, topological indices play a crucial role by providing numerical insights into molecular structures. These insights facilitate predictive correlations with chemical properties and reactivity, ultimately finding utility in areas like drug design and material sciences. Expanding on this, the study delves into the application of entropy‐based methodologies that originates from the arrangement of chemical structures. By assessing the complexity and other features of these structures, graph entropies are translated into information‐theoretic metrics. This article examines modified reverse degree‐based topological indices with its universal applicability to all degree‐based indices. The standout feature is the adaptable parameter “” effectively shaping the molecular graphs degree sequence to best fit each dataset with their unique physicochemical properties, distinguishing it from conventional fixed degree methodologies. Additionally, we investigate graph entropies and examine the impact of varying the parameter “” on entropy measures across a range of nanosheet structures. The research focuses on characterizing carbon nanosheets, employing effective (MCDM) multiple criteria decision‐making methods like VIKOR, TOPSIS, and SAW. Through these techniques, a comprehensive comparative analysis of the nanosheets is conducted with the aim of establishing optimized rankings for each type based on their unique attributes and characteristics.