Abstract: The atom-bond connectivity (ABC) index of a connected graph G=(V,E) is defined as ABC(G)=\sum\limits_{uv\in E(G)} \sqrt{\frac{d(u)+d(v)-2}{d(u)d(v)}}, where d(u) and d(v) are the degrees of u and u, respectively.  Atom-bond connectivity (ABC) index has been used in the study of the heat  formation in alkanes and the stability and the strain energy of alkane hydrocarbon. We present the lower and the upper bounds on ABC index of line and total graphs, and characterize graphs for which these bounds are tight.

Key words: atom-bond connectivity index, line graphs, total graphs