The Hosoya polynomial is crucial in graph theory, particularly for calculating distance-dependent indices like the Wiener index. This study concentrates on determining the Hosoya polynomial for the structure formed by the coronal product, or corona product, between the Cn cycle and the P2 path, which is denoted as Cn ⊙ P2. Based on the examination of vertex pair distances in this intricate diagram, an accurate formula for the Hosoya polynomial was developed. Moreover, formulas are outlined for determining the Wiener index for the structure Cn ⊙ P2, with separate considerations for scenarios where the number of cycle endpoints n is even and where it is odd. he study investigates the recognition of corona product graphs and develops an algorithm