On the Hosoya polynomial of the third type of the chain hex-derived network

A topological index plays an important role in characterising various physical properties, biological activities, and chemical reactivities of a molecular graph. The Hosoya polynomial is used to evaluate the distance-based topological indices such as the Wiener index, hyper-Wiener index, Harary index, and Tratch-Stankevitch-Zefirov index. In the present study, we determine a closed form of the Hosoya polynomial for the third type of the chain hex-derived network of dimension $n$ and derive the distance-based topological indices of the network with the help of their direct formulas and alternatively via using the obtained Hosoya polynomial. Finally, we graphically represent the computed distance-based topological indices and the Hosoya polynomial of the underlying network to comprehend their geometrical pattern. This study of the Hosoya polynomial and the corresponding indices can set the basis for more exploration into chain hex-derived networks and their properties.