HYPER-WIENER INDEX ON ROWS OF UNIT CELLS OF THE BCC GRID

Abstract

Hyper-Wiener index is a generalization of Wiener index. Hyper-Wiener index is also a distance-based graph invariant used as a structure-descriptor for predicting physicochemical properties of organic compounds. In this paper, we use lines of unit cells of the body-centred cubic grid: these grids have centre points of the unit cells and border vertices. Closed formulae are obtained to calculate the sum of the combined distances between pairs of border vertices, between border vertices and centres and between pairs of centres. Based on these formulae, the hyper-Wiener index of the given grid-graphs is computed. Some relations between our formula and integer sequences are also shown.