The atom bond connectivity index of a graph is a new topological index was defined by E. Estrada as ABC(G)  uvE (dG(u) dG(v) 2) / dG(u)dG(v) , where G d ( u ) denotes degree of vertex u. In this paper we present some bounds of this new topological index.

The B3LYP/6-31++G** density functional calculations were used to obtain minimum geometries and interaction energies between the molecular hydrogen and nanostructures of fullerenes, C20 (cage), C20 (bowl), C19Si (bowl, penta), C19Si (bowl, hexa). The H2 molecule is set as adsorbed in the distance of 3Å at vertical position from surface above the pentagonal and hexagonal sites of nanostructures. ...

the atom bond connectivity index of a graph is a new topological index was defined by e.estrada as abc(g)  uve (dg(u) dg(v) 2) / dg(u)dg(v) , where g d ( u ) denotes degreeof vertex u. in this paper we present some bounds of this new topological index.