Degree-Distance Based Topological Indices of Crystal Cubic Carbon Structure

Hong, Yang; Siddiqui, Muhammad Kamran; Arshad, Misbah; Naeem, Muhammad

doi:10.3390/atoms6040062

Cited by 9 publications

(6 citation statements)

References 18 publications

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“…Tis fnding suggests that incorporating the energy component of the topological index, rather than relying solely on the topological index itself, yields more accurate predictions of the physicochemical properties for any given molecular structure. Tis observation aligns with previous research [48][49][50][51], wherein the majority of studies focus on degree-based or distancebased topological indices and evaluate their signifcance. However, there is a lack of direct comparison between the energy and topological indices to determine the most accurate predictor.…”

Section: Mathematical Expression Vertex-degree Adjacency Matricessupporting

confidence: 85%

Graph Energy Variants and Topological Indices in Platinum Anticancer Drug Design: Mathematical Insights and Computational Analysis with DFT and QTAIM

Wazzan,

Ozalan

2023

Journal of Mathematics

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In this paper, we present a new approach that explores the application of graph energy variants in chemistry, specifically in the development of platinum anticancer drugs. While previous energy variants have been proposed without considering their direct relevance to chemistry, our study focuses on two key aspects. First, we investigate the correlation between seven degree-based and four distance-based topological indices and their corresponding energies in platinum anticancer drugs. Furthermore, we mathematically analyze the properties of these energies, establishing upper and lower bounds that can be generalized to other structures. Second, we examine the possibility of utilizing the energies of these topological indices as structural descriptors. Our research showcases promising results, suggesting potential improvements in the future manufacturing of anticancer drugs. In addition, we employ density functional theory D F T calculations to optimize the molecular structures of platinum anticancer drugs and identify local reactive sites using Fukui functions. Quantum theory of atoms in molecules Q T A I M was carried out at the bond critical point B C P , to reveal the nature of the intermolecular interactions in the investigated ten Pt anticancer drugs, especially, the nature of bonds between Pt atoms and their bond atoms. Overall, this study presents an innovative approach that bridges graph energies, topological indices, and DFT with the properties (physical and chemical) of platinum anticancer drugs, offering insights into their molecular properties and potential for enhanced drug design.

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Section: Mathematical Expression Vertex-degree Adjacency Matricessupporting

confidence: 85%

Graph Energy Variants and Topological Indices in Platinum Anticancer Drug Design: Mathematical Insights and Computational Analysis with DFT and QTAIM

Wazzan,

Ozalan

2023

Journal of Mathematics

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“…Zahid et al [37] studied about the fifth M-Zagreb indices as well as fifth M-polynomial of δ(n). Degree based topological indices of δ(n) has been computed by Yang et al [34]. Sharma et al [24] studied the degree-based multiplicative topological indices of the crystalline structure of cubic carbon for levels 3 to 10.…”

Section: Figure 2: Second Level Of Crystal Cubic Carbonmentioning

confidence: 99%

On mixed metric dimension of crystal cubic carbon structure

2023

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Chemical graph theory is a branch of mathematical chemistry which applies classic graph theory to chemical phenomena and entities. Graphs are extensively used in chemistry to recognise the structures of chemical compounds, with the vertices and edges denoting atoms and bonds respectively. Let Γ = (V, E) be a nth order connected graph. If the distance vectors to the vertices in an ordered subset H r of vertices can uniquely identify each vertex of the graph Γ, then the set H r is known as resolving set for the graph Γ. The resolving set H r with smallest cardinality serves as the metric dimension of graph Γ and this resolving set serves as the metric basis for Γ. A unique representation of chemical structures can be obtained using a resolving set. In this manuscript, the most important variant of metric dimension known as mixed metric dimension is taken into consideration and computed it for most important allotrope of carbon commonly known as crystal cubic carbon.

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“…Nevertheless, in cut down poor countries and locales (for instance, certain urban networks and countries in South America, Southeast Asia, Africa, and India), there is no sufficient money to settle reagents and apparatus which can be used to gauge the biochemical properties. For topological study of dendrimers, we refer [53][54][55][56][57][58][59][60][61][62][63][64][65][66]. 7.…”

Section: Gourava Indices For Dendrimersmentioning

confidence: 99%

Valency-Based Descriptors for Silicon Carbides, Bismuth(III) Iodide, and Dendrimers in Drug Applications

Virk

Nazar

et al. 2020

Journal of Chemistry

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Silicon carbide (SiC), also called carborundum, is a semiconductor containing silicon and carbon. Dendrimers are repetitively branched molecules that are typically symmetric around the core and often adopt a spherical three-dimensional morphology. Bismuth(III) iodide is an inorganic compound with the formula BiI3. This gray-black solid is the product of the reaction between bismuth and iodine, which once was of interest in qualitative inorganic analysis. In chemical graph theory, we associate a graph to a compound and compute topological indices that help us in guessing properties of the understudy compound. A topological index is the graph invariant number, calculated from a graph representing a molecule. Most of the proposed topological indices are related either to a vertex adjacency relationship (atom-atom connectivity) in the graph or to topological distances in the graph. In this paper, we aim to compute the first and second Gourava indices and hyper-Gourava indices for silicon carbides, bismuth(III) iodide, and dendrimers.

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Degree-Distance Based Topological Indices of Crystal Cubic Carbon Structure

Cited by 9 publications

References 18 publications

Graph Energy Variants and Topological Indices in Platinum Anticancer Drug Design: Mathematical Insights and Computational Analysis with DFT and QTAIM

Graph Energy Variants and Topological Indices in Platinum Anticancer Drug Design: Mathematical Insights and Computational Analysis with DFT and QTAIM

On mixed metric dimension of crystal cubic carbon structure

Valency-Based Descriptors for Silicon Carbides, Bismuth(III) Iodide, and Dendrimers in Drug Applications

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