Extremal Trees of the Eccentric Connectivity Index

Chemical indices are introduced to correlate chemical compounds' physical properties with their structures. Among recently introduced such indices, the eccentric connectivity index of a graph G is defined as {equation presented} is the degree of a vertex v and ec(v) is its eccentricity. The extremal values of {equation presented} have been studied among graphs with various given parameters. In this note we study trees with extremal values of the eccentric connectivity index with a given degree sequence. The extremal structures are identified, however they are not unique.