Hosoya Polynomials of Hexagonal Chains

Topological indices are used in mathematically modeling graphs and have applications in chemistry, where they can be used to relate structures of molecular compounds to their properties.The Hosoya polynomial can be used to determine distance-based topological indices like the Hosoya or Weiner index, which are widely-used descriptors of biological and chemical graphs, including molecular graphs made up of hexagons. Based on their configuration, hexagonal graphs represent specific polycyclic organic compounds that can be studied using the polynomial. In this research, we consider two types of hexagonal chains and obtain formulas for their Hosoya polynomials. We also investigate the Mycielskian constructions of the hexagonal chains and their formulas for the Hosoya polynomial of these graphs.