Chemical graph theory, a branch of graph theory, uses molecular graphs for its representation. In QSAR/QSPR studies, topological indices are employed to evaluate the bioactivity of chemicals. Degree-based entropy, derived from Shannon’s entropy, is a functional statistic influenced by the graph and the probability distribution of its vertex set, with informational graphs forming the basis of entropy concepts. Planar octahedron networks have diverse applications in pharmacy hardware and system management. This article explores the Benzenoid Planar Octahedron Network (\(BPOH(n)\)), Benzenoid Dominating Planar Octahedron Network (BDPOH(n)), and Benzenoid Hex Planar Octahedron Network (\(BHPOH(n)\)). We compute degree-based entropies, including Randić entropy, atom bond connectivity (ABC), and geometric arithmetic (GA) entropy, for the Benzenoid planar octahedron network.
