Chemical Relevance and Expected Values of K-Banhatti Indices ‎for Random Cyclodecane Chains

Cyclodecane, a remarkable cyclic hydrocarbon, comprises larger ‎molecular structures or polymers formed by interlinking multiple ‎cyclodecane rings. These interactions are crucial in ‎pharmacogenomics, as the strategic design of a compound decisively ‎influences its interactions with gene products, including enzymes and ‎receptors. In the dynamic field of mathematical chemistry, chemical ‎graph theory plays a crucial role in enhancing our understanding of ‎the complex properties of chemical compounds. Currently, one of the ‎most promising areas of research involves the calculation of ‎topological indices. Among these indices, the First K hyper-Banhatti ‎index, Second K hyper-Banhatti index, Modified first K-Banhatti index, ‎and Modified second K-Banhatti index serve as important topological ‎descriptors that significantly contribute to our analysis of the ‎physicochemical, biological, and structural characteristics of chemical ‎compounds. This article aims to determine the expected values of ‎these topological descriptors for random cyclodecane chains, ‎presenting our findings in significant numerical tables and insightful ‎graphical representations. Through this exploration, we aim to deepen ‎our appreciation of how these descriptors impact the fundamental ‎properties of chemical compounds, paving the way for future ‎discoveries in this compelling field.