Abstract
The augmented Zagreb index (AZI) is a molecular structure descriptor introduced about a decade ago. It is defined as
AZI = Sigma(uv) (d(u) d(v)/d(u) + d(v) - 2)(3),
where d(u) is the degree of the vertex u, and the summation goes over all pairs of adjacent vertices of the underlying molecular graph. Chemical applicability of AZI was tested in several studies, where it was found that in most cases AZI outperforms other structure descriptors of this type. This survey paper outlines extremal results and bounds on AZI that have been reported until now.