Zagreb connection indices in structure property modelling

One of the major branches of mathematical chemistry is the chemical graph theory that employs graph invariants to demonstrate chemical phenomena mathematically. Topological indices are numerical graph invariants derived from molecular graph representations of chemical compounds that are used in structure-property modelling. In a brief span of time, the Zagreb connection indices have garnered a lot of attention. The ultimate goal of the present report is to reveal the chemical significance of this variants of Zagreb index and to demonstrate their fascinating mathematical attributes. The chemical connection of the indices is examined by investigating their potential in structure-property modelling. To illustrate mathematical features, some crucial upper bounds for connection indices are computed with characterizing maximal structures. The maximal graphs for the class of connected, tree, bipartite and chain graphs are identified by means of connection indices in terms of graph order. Such characterization is quite useful in regulating molecular properties that the connection indices can predict.