A survey on terminal Wiener index

Abstract

The terminal Wiener index T W = T W (G) of a graph G is equal to the sum of distances between all pairs of pendent vertices of G . This distance–based molecular structure descriptor was put forward quite recently [I. Gutman, B. Furtula, M. Petrović, J. Math. Chem. 46 (2009) 522–531]. In this survey we outline the hitherto established properties of TW. In particular, we describe a simple method for computing TW of trees, characterize the trees with minimum and maximum TW, and provide a formula for calculating TW of thorn graphs.