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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.

Molecular graph; Chemical tree; Eccentric connectivity index (xi(C)); First Zagreb index (M(1)); Second Zagreb index (M(2))

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