Tutte polynomials for some chemical polycyclic graphs.

The Tutte polynomial is a classical polynomial graph invariant that provides important information about the structure of a graph. In this study, we focus on the Tutte polynomials for typical silicate molecular networks and benzenoid systems, and derive exact formulas for the considered polycyclic chemical graphs. We also determine the explicit closed-form analytic expressions for the number of spanning trees, connected spanning subgraphs, spanning forests, and acyclic orientations of these chemical polycyclic graphs. Our approach employs a combinatorial decomposition technique, which is a general method that can be easily extended to other 2-connected chemical polycyclic networks. This research contributes to a better understanding of the topological properties of chemical structures and has potential applications in chemistry and materials science. [ABSTRACT FROM AUTHOR]