Open AccessThe Eccentricity Version of Atom-Bond Connectivity Index of Linear Polycene Parallelogram Benzenoid ABC5(P(n,n))
Author(s) -
Wei Gao,
Mohammad Reza Farahani,
Muhammad Kamran Jamil
Publication year - 2016
Publication title -
acta chimica slovenica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.289
H-Index - 46
eISSN - 1580-3155
pISSN - 1318-0207
DOI - 10.17344/acsi.2016.2378
Subject(s) - parallelogram , topological index , combinatorics , vertex connectivity , vertex (graph theory) , molecular graph , connectivity , mathematics , atom (system on chip) , graph , physics , chemistry , computer science , hinge , classical mechanics , embedded system
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.