Analysis of Dendrimer Generation by Sombor Indices

Abstract

Dendrimers are highly branched, star-shaped macromolecules with nanometer-scale dimensions. Dendrimers are defined by three components: a central core, an interior dendritic structure (the branches), and an exterior surface with functional surface groups. Topological indices are numerical numbers that help us to understand the topology of different dendrimers and can be used to predict the properties without performing experiments in the wet lab. In the present paper, we computed the Sombor index and the reduced version of the Sombor index for the molecular graphs of phosphorus-containing dendrimers, porphyrin-cored dendrimers, PDI-cored dendrimers, triazine-based dendrimers, and aliphatic polyamide dendrimers. We also plotted our results by using Maple 2015 which help us to see the dependence of the Sombor index and reduced Sombor index on the involved parameters. Our results may help to develop better understanding about phosphorus-containing dendrimers, porphyrin-cored dendrimers, PDI-cored dendrimers, triazine-based dendrimers, and aliphatic polyamide dendrimers. Our results are also useful in the pharmaceutical industry and drug delivery.

Investigation of Dendrimer Structures by Means of K‐Banhatti Invariants

“…e first generation of dendrimers we studied in this paper is phosphoruscontaining dendrimers [2]. e graph of this generation is denoted by D 1 (p) where the number of stages is represented by p, see Figure 2.…”

“…e term dendrimers mean an arti cially generated nanomolecular structure which is highly useful in drug delivery [1,2]. Commonly, there are three types of dendrimers: (a) central core dendrimer, (b) interior surface dendrimer, and (c) outer surface dendrimers [3].…”

“…(i) Initiator core (ii) Interior layer (iii) Terminal functionalities Due to their molecular architecture, dendrimers display some undoubtedly enhanced physical and chemical properties when correlated with a conventional liner polymer [2,7]. e rare architectural layout of dendrimer, branching intensity, multivalency, globular, and well-de ned molecular weight implies that dendrimers are rare and excellent nanocarriers in medical utilization such as drug delivery, gene transfection, tumor therapy, etc.…”

Comparing Energy and Sombor Energy - An Empirical Study

“…The Sombor index SO is a recently designed VDB molecular structure descriptor, conceived by means of geometric considerations [8]. It promptly attracted much attention and its chemical applications (e.g., [1,2,20,23]) and mathematical properties (e.g., [5,16,21,29]) are being studied in a remarkably large number of papers (over 70 by the end of 2021). Also promptly, the concept of Sombor index was extended to Sombor energy and other spectral properties of the Sombor matrix [6,7,9,13,19,31].…”

Degree Based Topological Indices of a General Random Chain

“…In particular, Sombor index was recently introduced by Gutman in (Gutman 2021). Recent papers about Sombor index can be found in (Liu, Chen, Xiao, Fang, and Tang 2021;Chen, Li, and Wang 2021;Liu, You, Tang, and Liu 2021;Alikhani and Ghanbari 2021;Amin, Virk, Rehman, and Shah 2021;Das, C ¸evik, Cangul, and Shang 2021). Nowadays, the characterization of molecular structure through topological indices is performed using chemical graph theory, for this reason, this theory plays a vital role in the design of molecular structures with desired physico-chemical or biological properties.…”