Extremal properties of connected 4-cyclic graphs of a topological index related to chemical graphs.

Abstract

Augmented Zagreb index (AZI) is an important vertex-degree-based topological index with many applications especially in chemistry. In this article, minimum value of $AZI\left(G\right)$ is obtained and the corresponding extremal graph is characterized in the class of connected 4-cyclic graphs with seven or more vertices. These results can be used to characterize numerous chemical properties of chemical compounds having 4-cyclic structures.