Topological Wiener indices and polynomials of C₈₄ fullerene nanocage

The Wiener index is the most popular topological index used as an invariant molecular descriptor in the study of structures and physiochemical properties of molecules. Here, Wiener index and its modifications, hyper-Wiener and Harary indices, as well as Hosoya and hyper-Hosoya polynomials are studied over C₈₄ fullerene nanocage which is the third most abundant member of the higher fullerene series with two major structures known as stable C₈₄, D₂ (22) and D_2d (23). The computation of Wiener indices and polynomials of isomers C₈₄-D₂ (22) and C₈₄-D_2d (23) is implemented using graph algorithms which employ the isomer's molecular graphs. Our results show that the isomer C₈₄-D₂ (22) has greater Wiener and topological efficiency indices than isomer C₈₄-D_2d (23), which indicates that the isomer C₈₄-D_2d (23) has greater compactness and stability than isomer C₈₄-D₂ (22). These results are consistent with the experimental observations and further confirmed by the lower Harary index of isomer C₈₄-D₂ (22). The greater Wiener index of isomer C₈₄-D₂ (22) also suggests that its boiling point would be higher than that of isomer C₈₄-D_2d (23).