EXACT FORMULAS FOR THE FIRST ZAGREB ECCENTRICITY INDEX OF POLYCYCLIC AROMATIC HYDROCARBONS (PAHs)
MOHAMMAD REZA FARAHANI *
Department of Applied Mathematics, Iran University of Science and Technology (IUST), Narmak, 16844, Tehran, Iran.
*Author to whom correspondence should be addressed.
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)=ΣveV dv× 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)=ΣveV 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.
Keywords: Vertex degree, eccentricity, zagreb eccentricity indices, polycyclic aromatic hydrocarbons