Eccentricity Version of Atom-Bond Connectivity Index of Benzenoid Family ABC5(Hk). [30] (original) (raw)

Among topological descriptors, connectivity indices are very important and they have a prominent role in chemistry. One of them is atom-bond connectivity (ABC) index of a connected graph G=(V,E) and defined as where d denotes the degree of vertex v of G, that introduced by Furtula v and et.al. Also, in 1997, Sharma, Goswami and Madan introduced the eccentric connectivity index of the molecular graph G, (G) and defined as where ecc(u) is the largest distance between u and any other vertex v of G. And if then the distance d(x,y) between x and y is defined as the length of any shortest path in G connecting x and y. Now, by combine these above topological indexes, we now define a new version of ABC index as We denote this new index of a connected graph G (eccentric atom-bond connectivity index) by ABC (G). In this paper, we exhibit this new index and introduce 5 a closed formula of ABC for a famous family of Benzenoid. 5