Computing Degree-Based Topological Indices for Pentagonal Quintuple Chains

Abstract

In chemical graph theory, a molecular structure is modeled as a connected graph where vertices represent atoms and edges represent chemical bonds. A pentagonal chain is an organic network composed of fused five-membered cycles. While previous research has examined single, double, triple, and quadruple pentagonal configurations, this thesis addresses the structural metrics of the pentagonal quintuple chain graph ( ), which consists of five parallel linear layers of k pentagonal units [3]. Using the combinatorial edge partition method, we derive exact closed-form expressions for several primary degree-based topological indices, including the First and Second Zagreb indices, the Inverse Sum Index (ISI) index, the Atom-Bond Connectivity (ABC) index, and the Geometric-Arithmetic (GA) index. Furthermore, we characterize its algebraic structural asymmetry using the Total Irregularity Index (Irrt) and the Albertson Index (Alb) [4]. These results offer theoretical structural descriptors for predicting the physical and chemical properties of multi-layered five-membered cyclic networks in polymer and material science applications.