Relationship between the eccentric connectivity index and Zagreb indices

AbstractFor a (molecular) graph, the first Zagreb index M1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M2 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, ξC(G), is defined as, ∑vi∈V(G)diei, where di is the degree of a vertex vi and ei is its eccentricity. In this report we compare the eccentric connectivity index (ξC) and the Zagreb indices (M1 and M2) for chemical trees. Moreover, we compare the eccentric connectivity index (ξC) and the first Zagreb index (M1) for molecular graphs