Revan indices for the hexadentate-3-hydroxypyridinonesterminated dendrimers

Abstract

Dendrimers are highly ordered, unimolecular, monodisperse, micellar nanostructures, applied in various fields such as drug delivery, nanotechnology, and biomedical applications. Hexadentate 3-hydroxypyridinones-terminated dendrimers are used in iron binding and anti-microbial activities. In the molecular graph, atoms are the vertices, and the bonds are the edges. A graph G consists of a pair of nonempty sets of vertices V(G) and edges EG and dG(u) is the degree of a vertex u∈ V(G). In this study, multiple bonds were modeled as multi-edges, and all hydrogen atoms were included in the molecular graph, thereby reducing the assumptions of traditional computational methods. Here, different Revan indices, which are topological descriptors derived from graph theory, were computed for hexadentate-3-hydroxypyridinones-terminated dendrimers. The Revan degree rG(u) of a vertex u is defined as rG(u)=∆(G)+δ(G)−dG(u), where ∆(G) is the maximum degree and δ(G) is the minimum degree among the vertices in G. In this paper, the first, second, and third Revan indices, forgotten Revan index, hyper Revan index, atom-bond connectivity Revan index, product connectivity Revan index, sum connectivity Revan index, harmonic Revan index, and geometric arithmetic Revan index were computed for different generations of hexadentate 3-hydroxypyridinones-terminated dendrimers. The results demonstrate that the complex topology in dendrimers can be accurately represented with the Revan indices, and as a result, their structural properties can be better understood. This study underlines the importance of these topological indices in directing design and development toward advanced applications with dendrimer-based systems.