On geometric-arithmetic indices of single-walled zig-zag nanotubes

Topological indices have significant applications in QSAR/QSPR studies, which allow the prediction of physical ad chemical properties for many chemical structures based on statically validated analysis starting from a small data set. With regard to nano structures, the problem is that the calculation of an index, which is the first step towards its application, usually is an immensely complicated subject. Consequently, computing the value of the index, will be the central issue rather than considering its application or comparing with other easy-computing indices. In this paper, the arithmetic-geometric indices and their generalizations in relation to the single-walled zig-zag nanotubes TUHC_6 2p, q have been investigated. Our results proved that the values of these families of indices are approximately equal to the number of the edges of their molecular graphs. From this point of view, the computation of such indices, for single-walled Zig-Zag nanotubes, is worthless. Instead, an edge version of distance-based topological indices has been purposed. We found and compared relationships between some of these new indices and the total energy of TUHC_6 2p, q nanotubes.