ISSN print edition: 0366-6352 ISSN electronic edition: 1336-9075 Registr. No.: MK SR 9/7 Published monthly

On topological aspects of phosphorus dendrimers using edge cut method

Rashad Ismail, Shehnaz Akhter, Muhammad Kamran Siddiqui, Zahid Iqbal, and Farhana Yasmeen

Department of Mathematics, Faculty of Science and Arts, Mahayl Assir, King Khalid University, Abha, Saudi Arabia

E-mail: rismail@kku.edu.sa

Received: 21 February 2025  Accepted: 29 April 2025

Abstract:

Recent advancements in nanotechnology have enabled the synthesis of various nanostructures with controlled shapes, sizes, and chemo-physical properties, with dendrimers being the most well-characterized among them. Dendrimers have many applications due to their structural and functional versatility. Among the various classes of dendrimers, those that contain phosphorus in specific positions in their structures exhibit interesting properties and have a wide range of applications in pharmaceutical fields such as diagnosis, imaging, and drug delivery. Therapeutic agents can be either chemically connected or physically adsorbed onto the dendrimer surface or encapsulated within the dendritic architecture. Additionally, phosphorus dendrimers can be designed as drugs to treat infections, neurodegenerative diseases, inflammations, and cancer diseases. In the fields of chemical graph theory and mathematical chemistry, molecular structure descriptors are graph invariants that have multiple applications. These applications extend beyond drug discovery, chemistry, and toxicology to the theory of complex networks, where these invariants are utilized to express different structural properties of networks. The results of topological invariants are beneficial in quantitative structure-activity and structure–property relations (QSAR and QSAR ) for various chemical compounds. A wide range of topological invariants are known, particularly the bond-additive and distance-based invariants, commonly used in QSAR/QSPR studies. This article examines the various versions of Mostar, Szeged, and Padmakar–Ivan (PI) descriptors for the molecular graphs of two kinds of phosphorus dendrimers. We provide the precise values of these descriptors with the help of the cut method.

Keywords: Combinatorial Chemistry; Dendrimers; Mathematical Applications in Chemistry; Phosphorene; Polymers; Topology; Topological index; Szeged index; Mostar index; Padmakar–Ivan (PI) index; Dendrimers

Full paper is available at www.springerlink.com.

DOI: 10.1007/s11696-025-04106-4

Chemical Papers 79 (8) 5067–5085 (2025)