The Edge-Hyper-Wiener Index of Zigzag Single-Walled Nanotubes.

A topological index is a numerical value associated with a graph structure that has some correlation with corresponding physical property, chemical reaction or biological activity. To achieve much information and less degeneracy, many kinds of topological indices are defined on distances, degrees, countings, spectrums, etc. In this paper, we mainly study the edge-hyper-Wiener which is the distance-based index. It is the sum of the distances and the square of distances between all pairs of edges. Further, the exact expression of the edge-hyper-Wiener index of the zigzag single-walled nanotubes is given. [ABSTRACT FROM AUTHOR]