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

TL;DR

This paper characterizes extremal chemical graphs with maximum degree 3 that optimize 33 degree-based topological indices, revealing that only five graph families suffice for most indices, indicating limited variation in their extremal properties.

Contribution

It provides a comprehensive characterization of extremal graphs for 33 degree-based indices, showing that five graph families are sufficient for 29 of them, simplifying their analysis.

Findings

Five graph families characterize extremal graphs for most indices.

Extremal properties vary little among the indices.

Most indices are optimized by the same graph families.

Abstract

We consider chemical graphs that are defined as 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 five graph families are sufficient to characterize the extremal graphs of 29 of these 33 indices. In other words, the extremal properties of this set of degree-based topological indices vary very little.