A Note on Hyper-Wiener Index

Xuli Qi1, Bo Zhou2
1College of Mathematics and Information Science, Hebei Normal University, Hebei Key Laboratory of Computational Mathematics and Applications, Shijiazhuang 050024, P. R. China
2Department of Mathematics, South China Normal University, Guangzhou 510631, P. R. China

Abstract

The hyper-Wiener index is a graph invariant that is used as a structure descriptor for predicting physicochemical properties of organic compounds. We determine the n-vertex unicyclic graphs with the third smallest and the third largest hyper-Wiener indices for \(n\geq 5\).