title: Maximal unicyclic graphs with respect to new atom-bond connectivity index.
abstract: The concept of atom-bond connectivity (ABC) index was introduced in the chemical graph theory in 1998. The atom-bond connectivity (ABC) index of a graph G defined as (see formula in text) where E(G) is the edge set and di is the degree of vertex v(i) of G. Very recently Graovac et al. define a new version of the ABC index as (see formula in text) where n(i) denotes the number of vertices of G whose distances to vertex v(i) are smaller than those to the other vertex v(j) of the edge e = v(i) v(j), and n(j) is defined analogously. In this paper we determine the maximal unicyclic graphs with respect to new atom-bond connectivity index (ABC2).
authors.affiliation: Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea. kinkardas2003@googlemail.com
authors.forename: Kinkar Ch
authors.initials: KCh
authors.lastname: Das
authors.forename: Kexiang
authors.initials: K
authors.lastname: Xu
authors.forename: Ante
authors.initials: A
authors.lastname: Graovac