Spectral techniques to compute the Kirchhoff index and Wiener index of linear heptagonal cylindrical/Möbius networks

The Laplacian matrices are fundamental components in graph theory that provide the information about a graph's structure and its connectivity. To contribute significant insights into the characteristics and behaviour of heptagonal graph-based systems, the Kirchhoff index has applications in network designing, optimization, classification and visualization of graphs. To analyse these structural properties, the closed-form expressions for the Kirchhoff index and spanning trees of the linear cylindrical heptagonal chain Hn in terms of its Laplacian spectrum are computed. Unlike previous studies, which primarily rely on computational or numerical techniques, our method provides an analytical formulation that enhances the efficiency of resistance distance calculations. Furthermore, a relationship with the Wiener and Kirchhoff indices of Hn is proposed to enhance the understanding of the interplay among these graph parameters. These findings contribute to the advancement of spectral graph theory and its applications in complex network analysis.