The Ediz Eccentric Connectivity index and the Total Eccentricity Index of a Benzenoid System

Mohammad Reza Farahani

Abstract


Let G=(V,E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges. For u V(G), defined du be degree of vertex u. The eccentricity connectivity polynomial of a molecular graph G is defined as ECP(G;x)=  where ε(v) is the eccentricity of vertex v of G. Alternatively, the eccentric connectivity index is the first derivative of ECP(G;x) evaluated at x=1 and is equal to ξ(G)= Also, the total eccentricity index of G is defined as θ(G)= Recently, S. Ediz et al. defined Ediz eccentric connectivity index of G, Eξc(G), is defined as  where S(v) is the sum of degrees of all vertices adjacent to vertex v. In this paper, we compute these indices for Circumcoronene Series of Benzenoid Hk by Ring-Cut Method.


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