Tutte Polynomials and Graph Symmetries

Chbili, Nafaa; Alderai, Noura; Ali, Roba; AlQedra, Raghd

doi:10.3390/sym14102072

Cited by 2 publications

(1 citation statement)

References 28 publications

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“…Researchers are motivated by two primary objectives: firstly, identifying criteria that act as impediments for a graph to possess a specific symmetry and, secondly, comprehending the reliability of graph invariants in accurately reflecting graph properties. For instance, the study discussed in [1] focuses on examining the symmetries present in graphs and digraphs, extending to potential applications in knots, links, and the spatial arrangement of graphs in three-dimensional Euclidean space. The authors specifically investigate the interaction between algebraic invariants of graphs and their symmetries.…”

Section: Introductionmentioning

confidence: 99%

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

Wazzan

Ahmed

2023

Symmetry

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Molecular descriptors are essential in mathematical chemistry for studying quantitative structure–property relationships (QSPRs), 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. A 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 and 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 show 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 Its Applications in QSPR Studies of Octane and Its Isomers

Wazzan

Ahmed

2023

Symmetry

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show abstract

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.

show abstract

Tutte Polynomials and Graph Symmetries

Cited by 2 publications

References 28 publications

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

Symmetry-Adapted Domination Indices: The Enhanced Domination Sigma Index and Its 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

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