Exploring the Structural Information Content of Super-Polycyclic Aromatic Hydrocarbons via Degree-Based Graph Entropies

Graph entropy is an information-theoretic measure that offers a compact, inexpensive description of the structural information content of a molecule. This study examines two super-polycyclic aromatic hydrocarbons derived from hexa-peri-hexabenzocoronene, superphenalene and supertriphenylene . Although topological indices of these molecules have been reported, closed-form degree-based entropy expressions valid for general have not been derived; this multi-index treatment, cross-validated against independently reported HOMO–LUMO data, is the main novelty of the work. Using the edge partition based on end-vertex degrees, we derive closed-form expressions for eleven degree-based topological indices (Randić, reciprocal Randić, first and second Zagreb, atom-bond connectivity, geometric-arithmetic, harmonic, sum-connectivity, hyper-Zagreb, forgotten and augmented Zagreb). Within Shannon's entropy framework for edge-weighted graphs, we then obtain the corresponding degree-based and bond-wise entropies for ≥2, validated numerically for =2 to 10 and illustrated graphically. For every index and every , superphenalene has higher entropy than supertriphenylene, indicating a more evenly distributed edge-weight information. Since higher entropy is associated with greater stability, superphenalene is predicted to be kinetically more stable, in agreement with reported HOMO–LUMO gaps. The derived edge partitions may also support future QSAR/QSPR studies.