Journal of Applied Physical Science International

A topological index of a molecular graph G is a numeric quantity related to G which is invariant under symmetry properties of G. Let G be a molecular graph. The eccentric connectivity index ξ(G) is defined as ξ(G)=Σ_veV d_v× ε(v)where dv denotes the degree of a vertex v in G and ε(v) is the largest distance between u and any other vertex v of G. The First Zagreb eccentricity index is the eccentricity version of the classical First Zagreb index. The first Zagreb eccentricity index (EM₁(G)=Σ_veV ε(v)²) is defined as sum of squares of the eccentricities of the vertices. In this paper, exact formulas for the First Zagreb Eccentricity index of Polycyclic Aromatic Hydrocarbons (PAHs) is computed.