Structural mathematics of dendrimers through complementary topological indices

Abstract

Topological indices are key molecular descriptors in theoretical chemistry, nanotechnology and molecular modeling, linking structural and physicochemical properties. Recent advances in graph theory have broadened the application of these indices, revealing new mathematical insights and practical uses. This study investigates four complementary topological indices—recently proposed but still underexplored—in a special class of chemical graphs: dendrimers. Using combined approaches from graph theory and mathematical chemistry, we derive closed-form analytical expressions for the complementary Zagreb, Forgotten, geometric-arithmetic, and augmented Zagreb indices across four dendrimer families. These findings not only fill a theoretical gap but also establish quantitative links between dendrimer architecture and molecular properties.