Computing the Hosoya Index of Catacondensed Hexagonal Systems (2017)
The Hosoya index of a graph G is defined as Z (G) = P k≥0 m (G, k), where m (G, k) the number of ways in which k mutually independent edges can be selected in G. In this article we introduce the Hosoya vector of a graph at a given edge. Based on this concept and the recurrence relations known for Z, we give reduction formulas to compute the Hosoya index of any catacondensed hexagonal system via a product of 4×4 matrices with entries in N. As a consequence, we discuss the extremal value problem of the Hosoya index over certain subsets of the set of cataconsed hexagonal systems.