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.

Kinetics of magnetic flux in the thin mesoscopic ring biased by an external magnetic flux exhibits the ratchet-like behavior. The 'flux velocity', i.e. the averaged time derivative of magnetic flux produced by the ring, is a candidate for a novel characteristics of mesoscopic rings. Its global properties reflect the possibility of accommodating persistent currents in the ring. 1 Mesoscopic ring...

The vertex-edge Wiener polynomials of a simple connected graph are defined based on the distances between vertices and edges of that graph. The first derivative of these polynomials at one are called the vertex-edge Wiener indices. In this paper, we express some basic properties of the first and second vertex-edge Wiener polynomials of simple connected graphs and compare the first and second ve...

Kinetics of magnetic flux in a thin mesoscopic ring biased by a strong external magnetic field is described equivalently by dynamics of a Brownian particle in a tilted wash-board potential. The 'flux velocity', i.e. the averaged time derivative of the total magnetic flux in the ring, is a candidate for a novel characteristics of mesoscopic rings. Its global properties reflect the possibility of...

The bending of a carbon nanotube is studied by considering the structural evolution of a carbon nanotorus from elastic deformation to the onset of the kinks and eventually to the collapse of the walls of the nanotorus. The changes in the electronic properties due to non-local deformation are contrasted with those due to local deformation to bring out the subtle issue underlying the reason why t...