On structure-sensitivity of degree-based topological indices

•The structure sensitivity of topological indices is studied.•Degree-based topological indices are compared.•A measure of “smoothness” of a topological index is proposed.•A measure of “abruptness” of a topological index is proposed.

One of the general requirements for any topological index TI is that similar molecules have near-lying TI-values, which is referred to as “smoothness”. Curiously, however, smoothness of topological indices was until now never examined and never quantified. We now propose a pertinent mathematical model for this property, and undertake a comparative study of the structure-sensitivity of 12 degree-based topological indices by using trees.