Topological Wiener Indices and Polynomials of C<SUB>84</SUB> Fullerene Nanocage

Abstract

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 C 84 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 D2d (23). The computation of Wiener indices and polynomials of isomers C84–D2 (22) and C84–D2d (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-D2d (23), which indicates that the isomer C84–D2d (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–D2d (23).