Harmonic–Arithmetic Index for the Generalized Mycielskian Graphs and Graphenes With Curvilinear Regression Models of Benzenoid Hydrocarbons

The generalized Mycielskian graphs are known for their advantageous properties employed in interconnection networks in parallel computing to provide efficient and optimized network solutions. This paper focuses on investigating the bounds and computation of the harmonic–arithmetic index of the generalized Mycielskian graph of path graph, cycle graph, complete graph, and circulant graph. Furthermore, exploring the harmonic–arithmetic index of graphene provides insights into its structural properties, aiding in material design, predictive modeling, and understanding its behavior in various applications. Additionally, the study delves into analyzing the harmonic–arithmetic index of the curvilinear regression model concerning elucidating specific properties of benzenoid hydrocarbons, offering insights into their structural characteristics.