title: Three methods for calculation of the hyper-Wiener index of molecular graphs.
abstract: The hyper-Wiener index WW of a graph G is defined as WW(G) = (summation operator d (u, v)(2) + summation operator d (u, v))/2, where d (u, v) denotes the distance between the vertices u and v in the graph G and the summations run over all (unordered) pairs of vertices of G. We consider three different methods for calculating the hyper-Wiener index of molecular graphs: the cut method, the method of Hosoya polynomials, and the interpolation method. Along the way we obtain new closed-form expressions for the WW of linear phenylenes, cyclic phenylenes, poly(azulenes), and several families of periodic hexagonal chains. We also verify some previously known (but not mathematically proved) formulas.
authors.affiliation: Risk Assessment Division (7403), Office of Pollution Prevention and Toxics, US Environmental Protection Agency, Washington, DC 20460, USA.
authors.forename: Gordon
authors.initials: G
authors.lastname: Cash
authors.forename: Sandi
authors.initials: S
authors.lastname: Klavzar
authors.forename: Marko
authors.initials: M
authors.lastname: Petkovsek