Novel PI indices of hexagonal chains

The Padmakar-Ivan (PI) index of hexagonal chains (i.e., the molecular graphs of unbranched catacondensed benzenoid hydrocarbons) is examined. The index PI is a graph invariant defined as the summation of the sums of edges of n(eu) and n(ev) over all the edges of connected graph G, where n(eu) is the number of edges of G lying closer to u than to v and n(ev) is the number of edges of G lying closer to v than to u. An efficient calculation of formula for PI for hexagonal chains are put forward.