Three methods for calculation of the hyper-Wiener index of molecular graphs.
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.
Cash
Gordon
G
Risk Assessment Division (7403), Office of Pollution Prevention and Toxics, US Environmental Protection Agency, Washington, DC 20460, USA.
Klavzar
Sandi
S
Petkovsek
Marko
M