Characterizing the Degree-Kirchhoff, Gutman, and Schultz Indices in Pentagonal Cylinders and Möbius Chains

This article explores the characterization of the Degree-Kirchhoff, Gutman, and Schultz indices in pentagonal cylinders and Möbius chains, offering a deep dive into the topological structure of these graphs. It presents explicit expressions for these indices, derived using the Laplacian matrix approach and perturbation formulas, providing a novel method for handling complex Laplacian matrices. The article also establishes relationships between the Schultz and Gutman indices and compares the Gutman indices and the degree-Kirchhoff indices for different values of n. Furthermore, it discusses the Kirchhoff index's connection to the Wiener index and presents a comparative study of approaches used in earlier works. The article concludes with a discussion on the implications of these findings for graph theory, networking systems, and molecular chemistry, highlighting the potential for further research in these areas.