On the Hosoya index for the molecular graphs of helicenes

Abstract

The matching of an undirected graph G=(V,E) is a subset M of E such that no two edges of M are adjacent in G. The Hosoya index of a graph G is given by the number of all matching of G . This number is one of the most interesting topological index in chemistry. Helicenes are extremal hexagonal chains with a simple graph representation as an important subclass of benzenoid molecules. We obtain the exact formula for the Hosoya index of the molecular graphs of helicenes as a function of the number of hexagons in them.