Abstract
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 , ξ C ( G ) , is defined as, ∑ v i ∈ 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 ( ξ C ) and the Zagreb indices ( M 1 and M 2 ) for chemical trees. Moreover, we compare the eccentric connectivity index ( ξ C ) and the first Zagreb index ( M 1 ) for molecular graphs.
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