Eccentric Connectivity and Augmented Eccentric Connectivity indices of N-branched Phenylacetylenes Nanostar Dendrimers

A topological index of a molecular graph G is a numeric quantity related to G which isinvariant under symmetry properties of G. Let G be a molecular graph. The eccentricconnectivity index ξ(G) is defined as () deg() (), () Σ ∈ ξ = ε u V G G u u where deg(u) denotes the degree of vertex u in G and ε(u) is the largest distance between u and any other vertex v of G. The augmented eccentric connectivity index, A ξ(G) is defined as Σ ∈ ε ξ = () () () G () u V A u G M u, where M(u) denotes the product of degrees of all neighbors of vertex u. In this paper, exact formulas for the eccentric connectivity and augmented eccentric connectivity indices of an infinite family of nanostar dendrimer are computed.