Entropy measures of degree-based topological indices for hyper carbon nanotubes

Carbon nanotube structures have potential applications in nanoelectronics, molecular sensors, energy-storage devices, nanocomposites, and multi-terminal nanoscale interconnects. Motivated by their structural complexity, this paper investigates entropy measures of degree-based topological indices for a hyper armchair carbon nanotube (HCN) graph. The HCN graph is constructed by replacing the vertices of an armchair nanotube template with Y-shaped junction modules and its edges with armchair nanotube segments. Complete vertex-degree and vertex-degree-based edge partitions are established and checked against the order, size, and degree-sum identity of the graph. These partitions yield closed forms for the selected topological indices and for the Shannon entropies obtained by normalizing their edge contributions. Numerical comparisons show that the entropy values increase along the selected structural-parameter sequence, and the dominant degree class explains why the entropy values of different indices become close for larger HCN graphs.