On Vertex-Degree-Based Topological Indices of Cayley Digraphs of Rectangular Groups and Their Role as Molecular Descriptors - Pongpipat, Denpong; Nupo, Nuttawoot (Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya, 2026)
Let Cay(S,A) be the Cayley digraph of a finite rectangular group S with connection set A. We derive explicit formulas for several vertex-degree–based topological indices of these digraphs, including the Randić, Zagreb, sum-connectivity, geometric–arithmetic, atom–bond connectivity, and harmonic indices. The computations are reduced to Cayley digraphs of right groups, which simplifies the analysis. The underlying graphs are shown to be isomorphic to the hydrogen–included molecular graphs of cycloalkanes CnH2n. We prove that all considered indices depend linearly on the ring size n, exhibit stable growth, and differ only in their growth rates. Comparisons between related graph models illustrate the dependence of these indices on the underlying structure and support their interpretation as molecular descriptors, with possible relevance to QSAR/QSPR studies.