Introducing Structural Symmetry and Asymmetry Implications in Development of Recent Pharmacy and Medicine

Jäntschi, Lorentz

doi:10.3390/sym14081674

Cited by 10 publications

(2 citation statements)

References 59 publications

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“…While primarily applied in organic chemistry, these distance-based analyses offer potential applications in physical chemistry for molecules with high symmetry. Recent research articles (see References [3][4][5] and related works) have highlighted the significance of symmetry in graph theory, particularly in terms of graph invariants.…”

Section: Introductionmentioning

confidence: 99%

Symmetry-Adapted Domination Indices: The Enhanced Domination Sigma Index and Their Applications in QSPR Studies of Octane and Its Isomers

Wazzan¹,

Ahmed²

2023

Preprint

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Molecular descriptors are essential in mathematical chemistry for studying quantitative structure-property relationships (QSPR), and topological indices are a valuable source of information about molecular properties such as size, cyclicity, branching degree, and symmetry. Graph theory has played a crucial role in the development of topological indices and dominating parameters for molecular descriptors. The molecule graph, under graph isomorphism conditions, represents an invariant number, and the graph theory approach considers dominating sets, which are subsets of the vertex set where every vertex outside the set is adjacent to at least one vertex inside the set. The dominating sigma index, a topological index that incorporates the mathematical principles of domination topological indices and the sigma index, is applicable to some families of graphs, such as book graphs, windmill graphs, and some graph operations, which have exact values for this new index. To evaluate the effectiveness of the domination sigma index in QSPR studies, a comparative analysis was conducted to establish an appropriate domination index that correlates with the physicochemical properties of octane and its isomers. Linear and non-linear models were developed using the QSPR approach to predict the properties of interest, and the results showed that both the domination forgotten and domination first Zagreb indices exhibited satisfactory performance in comparison testing. Further research into QSAR/QSPR domination indices is required to build more robust models for predicting the physicochemical properties of organic compounds while maintaining the importance of symmetry.

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Section: Introductionmentioning

confidence: 99%

Symmetry-Adapted Domination Indices: The Enhanced Domination Sigma Index and Their Applications in QSPR Studies of Octane and Its Isomers

Wazzan¹,

Ahmed²

2023

Preprint

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show abstract

“…In most cases, determining the symmetries of a given object will lead to a better understanding of its physical and mathematical properties. The importance and significance of the concept of symmetry have been emphasized in many recent research articles, see [1][2][3] and references therein. This paper is concerned with symmetries of graphs and digraphs with possible extension to knots, links and spatial embedding of graphs in the three-dimensional Euclidean space.…”

Section: Introductionmentioning

confidence: 99%

Tutte Polynomials and Graph Symmetries

et al. 2022

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The Tutte polynomial is an isomorphism invariant of graphs that generalizes the chromatic and the flow polynomials. This two-variable polynomial with integral coefficients is known to carry important information about the properties of the graph. It has been used to prove long-standing conjectures in knot theory. Furthermore, it is related to the Potts and Ising models in statistical physics. The purpose of this paper is to study the interaction between the Tutte polynomial and graph symmetries. More precisely, we prove that if the automorphism group of the graph G contains an element of prime order p, then the coefficients of the Tutte polynomial of G satisfy certain necessary conditions.

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Least Squares for Generalized Gauss–Laplace Distribution of the Error in Certain Nonlinear Regressions with Perpendicular Offsets

Stoenoiu,

Jäntschi

2024

Springer Proceedings in Mathematics &Amp; Statistics

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Introducing Structural Symmetry and Asymmetry Implications in Development of Recent Pharmacy and Medicine

Abstract: Structural symmetry, anti-symmetry, or asymmetry represent a foundational property that, for chemical compounds, often determines their chemical and biological activity [...]

Cited by 10 publications

References 59 publications

Symmetry-Adapted Domination Indices: The Enhanced Domination Sigma Index and Their Applications in QSPR Studies of Octane and Its Isomers

Symmetry-Adapted Domination Indices: The Enhanced Domination Sigma Index and Their Applications in QSPR Studies of Octane and Its Isomers

Tutte Polynomials and Graph Symmetries

Least Squares for Generalized Gauss–Laplace Distribution of the Error in Certain Nonlinear Regressions with Perpendicular Offsets

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