Eccentric Connectivity Index of Chemical Trees

A. Ili\' c, I. Gutman, Eccentric Connectivity Index of Chemical Trees, MATCH Commun. Math. Comput. Chem. 65 (2011) 731-744 The eccentric connectivity index $\xi^c$ is a distance--based molecular structure descriptor that was recently used for mathematical modeling of biological activities of diverse nature. We prove that the broom has maximum $\xi^c$ among trees with a fixed maximum vertex degree, and characterize such trees with minimum $\xi^c$\,. In addition, we propose a simple linear algorithm for calculating $\xi^c$ of trees.