This paper is concerned with the general atom-bond sum-connectivity index ABSγ, which a generalization of recently proposed index, where γ any real number. For connected graph G more than two vertices, number ABSγ(G) defined as sum (1−2(dx+dy)−1)γ over all edges xy G, dx and dy represent degrees vertices x y respectively. −10≤γ≤10, significance ABSγ examined on data set twenty-five benzenoid hy...

The atom-bond connectivity (ABC) index is a recently introduced topological index, defined as ABC(G) = ∑ uv∈E(G) √ du+dv−2 dudv , where du (or dv) is the degree the vertex u (or v). The ABC index of benzenoid systems and phenylenes are computed, a simple relation is established between the atom-bond connectivity index of a phenylene and the corresponding hexagonal squeeze in this paper. Mathema...

The atom-bond connectivity index is a useful topological index in studying the stability of alkanes and the strain energy of cycloalkanes. In this paper some inequalities for the atom-bond connectivity index of a series of graph operations are presented. We also prove our bounds are tight. As an application, the ABC indices of C4 nanotubes and nanotori are computed. © 2011 Elsevier B.V. All rig...

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 w...

Among topological descriptors connectivity topological indices are very important and they have a prominent role in chemistry. One of them is atom-bond connectivity (ABC) index defined as ABC(G)= [formula:see text], in which degree of vertex v denoted by dv . Recently, a new version of atom-bond connectivity (ABC4) index was introduced by M. Ghorbani et.al in 2010 and is defined as ABC4(G)= [fo...