The Eccentricity Version of Atom-Bond Connectivity Index of Linear Polycene Parallelogram Benzenoid ABC5(P(n,n))
Wei Gao, Mohammad Reza Farahani, Muhammad Kamran Jamil · Acta chimica slovenica · 2016
Among topological descriptors, connectivity indices are very important and they have a prominent role in chemistry. The atom-bond connectivity index of a connected graph G is defined as ABC(G) = ∑(uv ∈E (G)) √((du + dv - 2)/dudv), where dv denotes the degree of vertex v of G and the eccentric connectivity index of the molecular graph G is defined as ξ(G) = ∑(v ∈V) dv × ε(v), where ε(v) is the largest distance between v and any other vertex u of G. Also, the eccentric atom-bond connectivity index of a connected graph G is equal to ABC5(G) =∑(uv ∈E (G)) √((ε(u) + ε(v) - 2)/(ε(u)ε(v))). In this present paper, we compute this new Eccentric Connectivity index for an infinite family of Linear Polycene Parallelogram Benzenoid.