About the Zagreb Indices

The original Zagreb indices and some of their variants, such as the modified Zagreb indices, variable Zagreb indices, reformulated original Zagreb indices, reformulated modified Zagreb indices, Zagreb indices as complexity indices, general Zagreb indices, Zagreb indices for heterocyclic systems, Zagreb co-indices, are outlined. Some interesting properties of the Zagreb indices, depending on the structure of molecular (chemical) graphs, are mentioned. Zagreb indices of line graphs and their connection with certain walks on graphs are discussed. The relationships between the Zagreb indices and some of the earliest molecular descriptors such as the Platt index (introduced in 1947) and Gordon-Scantlebury index (introduced in 1964) are presented. So-called Zagreb co-indices are briefly mentioned. Analytical formulas for computing Zagreb indices of several homologous structures are also given.