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The eccentric connectivity index $\xi^c$ is a distance--based molecularstructure descriptor that was recently used for mathematical modeling ofbiological activities of diverse nature. We prove that the broom has maximum$\xi^c$ among trees with a fixed maximum vertex degree, and characterize suchtrees with minimum $\xi^c$\,. In addition, we propose a simple linear algorithmfor calculating $\xi^c$ of trees.

Eccentric Connectivity Index of Chemical Trees