Full paper
Adnan Asghar 1 *
1 Department of Chemicals and Materials Engineering, University of Alberta, Edmonton, Canada
* Correspondence to: adnanasghar14041985@gmail.com
pp. 43-75
Abstract
A topological index is a numerical value derived from the molecular graph structure, widely used to characterize molecular topology and predict chemical, physical, or bio- logical properties. This study presents an in-depth exploration of neighborhood degree- based topological indices within the realm of chemical graph theory, focusing on four diverse molecular structures: the Enhanced Mesh Network, Triangular Mesh Network, Star of Silicate Network, and Rhenium Trioxide Lattice. Employing advanced math- ematical techniques, including the NM Polynomial and calculus operators, in tandem with computational tools like Maple 2020 and MATLAB, we meticulously analyze the structural intricacies and connectivity patterns inherent in each molecular architecture. The calculated topological indices provide a quantitative framework for characterizing the unique graph-theoretical features of these complex molecular systems. Visualization through MATLAB facilitates a nuanced understanding of the molecular topology. This research not only advances the field of chemical graph theory but also opens avenues for tailoring molecular designs with implications for materials science, catalysis, and network analysis.
A topological index is a numerical value derived from the molecular graph structure, widely used to characterize molecular topology and predict chemical, physical, or bio- logical properties. This study presents an in-depth exploration of neighborhood degree- based topological indices within the realm of chemical graph theory, focusing on four diverse molecular structures: the Enhanced Mesh Network, Triangular Mesh Network, Star of Silicate Network, and Rhenium Trioxide Lattice. Employing advanced math- ematical techniques, including the NM Polynomial and calculus operators, in tandem with computational tools like Maple 2020 and MATLAB, we meticulously analyze the structural intricacies and connectivity patterns inherent in each molecular architecture. The calculated topological indices provide a quantitative framework for characterizing the unique graph-theoretical features of these complex molecular systems. Visualization through MATLAB facilitates a nuanced understanding of the molecular topology. This research not only advances the field of chemical graph theory but also opens avenues for tailoring molecular designs with implications for materials science, catalysis, and network analysis.Keywords
topological index, degree, Enhanced Mesh, Triangular Mesh, Star of Silicate Network, Rhenium Trioxide Lattice
topological index, degree, Enhanced Mesh, Triangular Mesh, Star of Silicate Network, Rhenium Trioxide Lattice
First published: 17.02.2025
