Extremal chemical graphs of maximum degree at most 3 for 33 degree-based topological indices

A large number of degree-based topological indices have been pro- posed in the literature to study properties of graphs modeling molecular structures. One can wonder if all these invariants are really distinct from an extremal perspective. In this talk, we will give a clear answer for connected graphs of maximum degree at most 3. We characterize the extremal graphs, meaning those that maximize or minimize 33 degree- based topological indices. This study shows that ve graph families are sucient to characterize the extremal graphs of 29 of these 33 indices. In other words, the extremal properties of this set of degree-based topolog- ical indices vary very little.