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 xi(C()G) = Sigma(v is an element of v(G)) deg(v)ec(v), where deg(v) is the degree of a vertex v and ec(v) is its eccentricity. The extremal values of xi(C) (G) 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.
"Extremal Trees of the Eccentric Connectivity Index."
Ars Combinatorica, 122: 55-64.