Some inequalities for the atom-bond connectivity index of graph operations

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 ABCABC indices of C4C4 nanotubes and nanotori are computed.