DETOUR INDEX FOR BODY-CENTRED CUBIC GRID WITH UNIT CELLS CONNECTED IN A ROW

Abstract

The detour index is equal to the sum of the length of the longest path between each pair of vertices of a connected graph. In theoretical chemistry, molecular structure descriptors are used to compute properties of chemical compounds. Among them Wiener, Szeged and detour indices play significant roles in anticipating chemical phenomena. In this paper, we compute the detour index of the graph of unit cells of the body-centred cubic lattice connected in a row. A closed formula is proven with the parameter of the number of unit cells.