Relationship between the eccentric connectivity index and Zagreb indices

For a (molecular) graph, the first Zagreb index M-1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M-2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. If G is a connected graph with vertex set V (G), then the eccentric connectivity index of G, xi(C)(G), is defined as, Sigma(vi is an element of V(G)) d(i)e(i), where d(i) is the degree of a vertex v(i) and e(i) is its eccentricity. In this report we compare the eccentric connectivity index (xi(C)) and the Zagreb indices (M-1 and M-2) for chemical trees. Moreover, we compare the eccentric connectivity index (xi(C)) and the first Zagreb index (M-1) for molecular graphs. (C) 2011 Elsevier Ltd. All rights reserved.