Graph-theoretical approaches to entropy in Cuâ‚‚O crystalline structures: implications for biomedical and energy applications

Abstract

In molecular science, understanding the intricate connections between molecular structures and their biomedical and pharmacological properties has been a focal point of research, aided by experimental and computational approaches. A key tool in this exploration is the use of Topological Indices, which are numerical descriptors that reveal fundamental characteristics of molecular frameworks. These indices are particularly crucial in predicting the biological activity of new chemical compounds and pharmaceuticals by quantifying weighted entropies. In this study, we examine the concept of graph entropy in relation to the topological properties of the copper oxide crystalline structure (𝐶𝑢₂𝑂[𝑖,𝑗,𝑡]). Our goal is to unravel the mathematical complexity of 𝐶𝑢₂𝑂[𝑖,𝑗,𝑡] by integrating entropy with various topological indices, including weighted measures. We also present a graphical comparison that illustrates the interplay between these computed indices and their corresponding entropies, offering new insights into the structural and mathematical elegance of 𝐶𝑢₂𝑂[𝑖,𝑗,𝑡]. This analysis broadens our understanding of the material’s potential applications across fields such as chemical sensors, solar cells, photocatalysis, and energy storage, where the unique crystallography of 𝐶𝑢₂𝑂 plays a pivotal role.