Effect of a Ring onto Values of Eigenvalue–Based Molecular Descriptors

Redžepović, Izudin; Radenković, Slavko; Furtula, Boris

doi:10.3390/sym13081515

Cited by 3 publications

(3 citation statements)

References 25 publications

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“…In other words, the symmetry or asymmetry of the graph structures affects the properties of the associated characteristic polynomials. In the views of applicational aspects involving the characteristic polynomials, symmetries and graphs in the domain of chemical sciences, the molecules can be represented in numerical forms representing the underlying graph structures with varying symmetries, and the chemical properties of the molecules vary accordingly [21,22].…”

Section: Pl-homeomorphism Self-homeomorphism and Applicational Aspectsmentioning

confidence: 99%

Topological Deformations of Manifolds by Algebraic Compositions in Polynomial Rings

Bagchi

2024

Symmetry

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The interactions between topology and algebraic geometry expose various interesting properties. This paper proposes the deformations of topological n-manifolds over the automorphic polynomial ring maps and associated isomorphic imbedding of locally flat submanifolds within the n-manifolds. The manifold deformations include topologically homeomorphic bending of submanifolds at multiple directions under algebraic operations. This paper introduces the concept of a topological equivalence class of manifolds and the associated equivalent class of polynomials in a real ring. The concepts of algebraic compositions in a real polynomial ring and the resulting topological properties (homeomorphism, isomorphism and deformation) of manifolds under algebraic compositions are introduced. It is shown that a set of ideals in a polynomial ring generates manifolds retaining topological isomorphism under algebraic compositions. The numerical simulations are presented in this paper to illustrate the interplay of topological properties and the respective real algebraic sets generated by polynomials in a ring within affine 3-spaces. It is shown that the coefficients of polynomials generated by a periodic smooth function can induce mirror symmetry in manifolds. The proposed formulations do not consider the simplectic class of manifolds and associated quantizable deformations. However, the proposed formulations preserve the properties of Nash representations of real algebraic manifolds including Nash isomorphism.

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Section: Pl-homeomorphism Self-homeomorphism and Applicational Aspectsmentioning

confidence: 99%

Topological Deformations of Manifolds by Algebraic Compositions in Polynomial Rings

Bagchi

2024

Symmetry

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“…Years ago, a method for assessing the effect of a ring on the value of the graph energy was presented [23]. Recently, this approach has been expanded to other eigenvalue‐based indices [24].…”

Section: Introductionmentioning

confidence: 99%

Partition of topological indices of benzenoid hydrocarbons into ring contributions

Redžepović

Đorđević

Brezovnik

et al. 2023

Int J of Quantum Chemistry

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This work presents a simple method for partitioning the bond-additive and atoms-pairadditive distance-based topological indices of plane graphs into the sum of contributions of inner faces. The proposed method is applied to decompose several topological indices (Wiener, hyper-Wiener, Tratch-Stankevich-Zefirov, Balaban, and Szeged indices) into the ring contributions for a series of benzenoid systems. It was found that the employed ring partitioning scheme is providing an accurate assessment of the dominant cyclic conjugation modes in the studied benzenoid hydrocarbons. Thus, the proposed method can be used as the alternative for the quantum-chemistry-based aromaticity indices which are significantly more computationally demanding.

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“…The energy E(G) is the sum of absolute A-eigenvalues of G. A significant amount of research has been conducted on this idea [16]. Following the potential applications of the A-spectrum, numerous topological indices were investigated from a spectral perspective by modifying the classical adjacency matrix accordingly [19][20][21][22][23][24][25][26][27][28][29]. Zhou and Trinajstić [30] introduced the matrix corresponding to the sum-connectivity index and studied associated energy in 2010.…”

Section: Introductionmentioning

confidence: 99%

On Neighborhood Inverse Sum Indeg Energy of Molecular Graphs

et al. 2022

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The spectral graph theory explores connections between combinatorial features of graphs and algebraic properties of associated matrices. The neighborhood inverse sum indeg (NI) index was recently proposed and explored to be a significant molecular descriptor. Our aim is to investigate the NI index from a spectral standpoint, for which a suitable matrix is proposed. The matrix is symmetric since it is generated from the edge connection information of undirected graphs. A novel graph energy is introduced based on the eigenvalues of that matrix. The usefulness of the energy as a molecular structural descriptor is analyzed by investigating predictive potential and isomer discrimination ability. Fundamental mathematical properties of the present spectrum and energy are investigated. The spectrum of the bipartite class of graphs is identified to be symmetric about the origin of the real line. Bounds of the spectral radius and the energy are explained by identifying the respective extremal graphs.

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Effect of a Ring onto Values of Eigenvalue–Based Molecular Descriptors

Cited by 3 publications

References 25 publications

Topological Deformations of Manifolds by Algebraic Compositions in Polynomial Rings

Topological Deformations of Manifolds by Algebraic Compositions in Polynomial Rings

Partition of topological indices of benzenoid hydrocarbons into ring contributions

On Neighborhood Inverse Sum Indeg Energy of Molecular Graphs

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