Plavsic

A novel general formula for the hyper-Wiener index of acyclic structures Dejan Plavsic^a, Nella Lers^b, and Katica Sertic-Bionda^b dplavsic@rudjer.irb.hr ^aThe Ruder Boskovic Institute, P.O.B. 1016, HR-10001 Zagreb, The Republic of Croatia ^bFaculty of Chemical Engineering and Technology, University of Zagreb, HR-10000 Zagreb, The Republic of Croatia

The hyper-Wiener index was recently introduced by Randi?. It is shown analytically that the hyper-Wiener index, the Wiener number and the W´/W index are closely related graph-theoretical invariants for acyclic structures. On the basis of this relationship the general analytical expression for the hyper-Wiener index of acyclic structures is derived. The formula provides an easy method to calculate the hyper-Wiener index for any connected acyclic graph.