Wiener and Hyper‐Wiener Indices of Polygonal Cylinder and Torus

Peng, Zhi-Ba; Nizami, Abdul Rauf; Iqbal, Zaffar; Munir, Mobeen; Ahmed, Hafiz Muhammad Waqar; Liu, Jia‐Bao

doi:10.1155/2021/8882646

Cited by 5 publications

(3 citation statements)

References 28 publications

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“…In their paper titled "On Conjecture of Merri ed Simmons Index ," Suresh Elumalai and colleagues provided a clear explanation of this matter [13]. The Wiener Index is de ned as half of the total of distances between every pair of atoms in a molecular graph [14]. Mathematically, for a graph G with n vertices (atoms)…”

Section: Methodsmentioning

confidence: 99%

Computation of Wiener and Hyper Wiener Indices in Several B-Complex Vitamins

Greeta,

Jayalalitha

2024

Preprint

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B vitamins are crucial for the proper functioning of our body. Vitamin B complex, comprising eight essential vitamins, supports growth and sustains energy levels. Graph theory aids chemists in systematically molecular modeling structures and reactions. Topological indices serve as mathematical descriptors, analyzing physicochemical properties. In this work, four B complex Vitamins—B1, B2, B3, and B6—are examined. The investigation centers on utilizing the distance matrix. It computes both the Wiener Index and Hyper Wiener Index, providing valuable perceptions toward the structural attributes of these vitamins. The outcomes of these metrics are systematically compared with the respective molecular weights of the vitamins. This comparison offers a comprehensive understanding of their chemical characteristics. It delves into the relationship among the structural features, topological indices, and molecular weights of essential B-complex vitamins. This paper explores enhancing our understanding of their biochemical roles and potential applications in health and medicine.

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Section: Methodsmentioning

confidence: 99%

Computation of Wiener and Hyper Wiener Indices in Several B-Complex Vitamins

Greeta,

Jayalalitha

2024

Preprint

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“…Diferent versions of Wiener indices for symmetric molecular structures were computed in [7]. In a recent work, Peng et al [8] derived Wiener and hyper-Wiener indices of polygonal cylinder and torus. In 1989, Schultz introduced a topological index known as Schultz index [9] which is a blend of degree and distance.…”

Section: Introductionmentioning

confidence: 99%

Topological Indices of Total Graph and Zero Divisor Graph of Commutative Ring: A Polynomial Approach

Mondal

Imran

De³

et al. 2023

Complexity

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The algebraic polynomial plays a significant role in mathematical chemistry to compute the exact expressions of distance-based, degree-distance-based, and degree-based topological indices. The topological index is utilized as a significant tool in the study of the quantitative structure activity relationship (QSAR) and quantitative structures property relationship (QSPR) which correlate a molecular structure to its different properties and activities. Graphs containing finite commutative rings have wide applications in robotics, information and communication theory, elliptic curve cryptography, physics, and statistics. In this article, the topological indices of the total graph T ℤ n n ∈ ℤ + , the zero divisor graph Γ ℤ r n ( r is prime, n ∈ ℤ + ), and the zero divisor graph Γ ℤ r × ℤ s × ℤ t ( r , s , t are primes) are computed using some algebraic polynomials.

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“…Randic also improved the Weiner indices calledhyper-Wiener indices [27]. The hyper-Wiener indices, ww is given by equation (3b) [28]:…”

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confidence: 99%

Topology Molecular Indices Relationship of Electronic Properties of N-Alkanes and Branched Alkanes

Alias

Zabidi

Zakaria

et al. 2023

Iraqi Journal of Science

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Eight electronic properties; HUMO, LUMO, HOMO-LUMO energy gap, dipole moment point-charge, dipole moment hybrid, molecular weight, heat of formation and zero-point energy of 60 normal and branched alkanes were examined using topology molecular indices. All the electronic properties were calculated using semi-empirical self-consistent molecular orbital theory. The relationship of electronic calculation properties with seven models of topology indices based on degree and/or distance were obtained in terms of their correlation, regression and principal component analysis. Most of the properties were well-modelled (r2 > 0.82) by topology molecular indices except the dipole moment point-charge and hybrid. The PCA resulted in 7 properties and 60 structures of alkanes that produced two principal components with eigenvalues of greater than 1. The first principal component explained 60.388%, while the second principal component explained 26.457%, bringing a cumulative value of 86.845% to the data variation.

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Wiener and Hyper‐Wiener Indices of Polygonal Cylinder and Torus

Cited by 5 publications

References 28 publications

Computation of Wiener and Hyper Wiener Indices in Several B-Complex Vitamins

Computation of Wiener and Hyper Wiener Indices in Several B-Complex Vitamins

Topological Indices of Total Graph and Zero Divisor Graph of Commutative Ring: A Polynomial Approach

Topology Molecular Indices Relationship of Electronic Properties of N-Alkanes and Branched Alkanes

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