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Study of Molecules in the Light of Spectral Graph Theory

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A special issue of Molecules (ISSN 1420-3049). This special issue belongs to the section "Computational and Theoretical Chemistry".

Deadline for manuscript submissions: closed (28 February 2023) | Viewed by 17912

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Special Issue Editor

Prof. Dr. Jia-Bao Liu

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Guest Editor

School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
Interests: graph theory; combinatorial chemistry; network topology; modeling; statistical analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

When the membrane vibration problem is treated by approximative solving of the associated partial differential equation, the eigenvalues of the graph of a discrete model of the membrane are considered. Molecular graph spectra, or the spectra of certain matrices closely related to adjacency matrices, exist in a number of statistical physics problems and in the field of quantum chemistry.

The dimer problem is concerned with the study of the thermodynamic properties of a system of diatomic molecules ("dimers") adsorbed on a crystal's surface. A two-dimensional lattice provides the most advantageous locations for atom adsorption on such a surface, and a dimer can occupy two nearby points. All possible ways for dimers to be stacked on the lattice without overlapping one another must be enumerated, in order to fill every lattice point. The dimer problem on a square lattice is similar to enumerating all the ways a chessboard of dimension ( being even) can be covered by dominoes so that each domino covers two adjacent squares of the chessboard and all squares are covered in this way. A particular adsorption surface can be related to a molecular graph. The molecular graph's vertices (atoms) indicate the points that are most conducive to adsorption. If the matching points can be occupied by a dimer, then the two vertices (atoms) of a molecular graph are adjacent (bonded). A 1-factor in the related molecular graph is determined by the arrangement of dimers on the surface, and vice versa. As a result, the dimer problem is reduced to figuring out how many 1-factors there are in a molecular graph. The examination of walks in matching molecular graphs and molecular graph eigenvalues is required for the enumeration of 1-factors.

Quantum chemists and chemical graph theorists use the symbol to represent the total -electron energy of hydrocarbon-conjugated molecules. The total -electron energy of hydrocarbon-conjugated molecules is calculated by using the Huckel molecular orbital (HMO) model, which is the oldest technique to study quantum chemical characteristics for large polycyclic hydrocarbon-conjugated molecules. Many years ago, it was documented that the different -electron energies of hydrocarbon-conjugated molecules of the HMO model, including, can be determined by the eigenvalues of the molecular graph. Furthermore, it is well known that the topological indices of molecular graphs are interrelated. In fact, a topological index correlates certain physicochemical properties of chemical compounds with molecular structure, such as boiling point and stability energy. Such an index, created by converting a chemical network into a numeric quantity associated with a molecular graph, describes the structure’s topology and is an invariant understructure that preserves mappings.

This Special Issue aims to offer an opportunity for researchers to discuss and share their own ideas in investigating the spectral properties associated with different matrices of various molecules. We would like for this Special Issue to enable us to solve some particular problems in statistical physics and quantum chemistry.

Prof. Dr. Jia-Bao Liu
Guest Editor

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Keywords

molecular graph
eigenvalues of molecular graph
energy of molecular graph
laplacian energy of molecular graph
topological indices of molecular graph
spectral graph theory in chemistry
spectral graph theory in statistical physics

Published Papers (17 papers)

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Research

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21 pages, 5924 KiB

Open AccessArticle

Algorithmic Graph Theory, Reinforcement Learning and Game Theory in MD Simulations: From 3D Structures to Topological 2D-Molecular Graphs (2D-MolGraphs) and Vice Versa

by Sana Bougueroua, Marie Bricage, Ylène Aboulfath, Dominique Barth and Marie-Pierre Gaigeot

Molecules 2023, 28(7), 2892; https://doi.org/10.3390/molecules28072892 - 23 Mar 2023

Cited by 3 | Viewed by 2119

Abstract

This paper reviews graph-theory-based methods that were recently developed in our group for post-processing molecular dynamics trajectories. We show that the use of algorithmic graph theory not only provides a direct and fast methodology to identify conformers sampled over time but also allows to follow the interconversions between the conformers through graphs of transitions in time. Examples of gas phase molecules and inhomogeneous aqueous solid interfaces are presented to demonstrate the power of topological 2D graphs and their versatility for post-processing molecular dynamics trajectories. An even more complex challenge is to predict 3D structures from topological 2D graphs. Our first attempts to tackle such a challenge are presented with the development of game theory and reinforcement learning methods for predicting the 3D structure of a gas-phase peptide. Full article

(This article belongs to the Special Issue Study of Molecules in the Light of Spectral Graph Theory)

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28 pages, 3429 KiB

Open AccessArticle

Comparative Study of Molecular Descriptors of Pent-Heptagonal Nanostructures Using Neighborhood M-Polynomial Approach

by D. Antony Xavier, Muhammad Usman Ghani, Muhammad Imran, Theertha Nair A., Eddith Sarah Varghese and Annmaria Baby

Molecules 2023, 28(6), 2518; https://doi.org/10.3390/molecules28062518 - 9 Mar 2023

Cited by 4 | Viewed by 2432

Abstract

In this article, a novel technique to evaluate and compare the neighborhood degree molecular descriptors of two variations of the carbon nanosheet

C_{5} C_{7} (a, b)

is presented. The conjugated molecules follow the graph spectral theory, in terms [...] Read more.

In this article, a novel technique to evaluate and compare the neighborhood degree molecular descriptors of two variations of the carbon nanosheet

C_{5} C_{7} (a, b)

is presented. The conjugated molecules follow the graph spectral theory, in terms of bonding, non-bonding and antibonding Ruckel molecular orbitals. They are demonstrated to be immediately determinable from their topological characteristics. The effort of chemical and pharmaceutical researchers is significantly increased by the need to conduct numerous chemical experiments to ascertain the chemical characteristics of such a wide variety of novel chemicals. In order to generate novel cellular imaging techniques and to accomplish the regulation of certain cellular mechanisms, scientists have utilized the attributes of nanosheets such as their flexibility and simplicity of modification, out of which carbon nanosheets stand out for their remarkable strength, chemical stability, and electrical conductivity. With efficient tools like polynomials and functions that can forecast compound features, mathematical chemistry has a lot to offer. One such approach is the M-polynomial, a fundamental polynomial that can generate a significant number of degree-based topological indices. Among them, the neighborhood M-polynomial is useful in retrieving neighborhood degree sum-based topological indices that can help in carrying out physical, chemical, and biological experiments. This paper formulates the unique M-polynomial approach which is used to derive and compare a variety of neighborhood degree-based molecular descriptors and the corresponding entropy measures of two variations of pent-heptagonal carbon nanosheets. Furthermore, a regression analysis on these descriptors has also been carried out which can further help in the prediction of various properties of the molecule. Full article

(This article belongs to the Special Issue Study of Molecules in the Light of Spectral Graph Theory)

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15 pages, 3188 KiB

Open AccessArticle

Molecular-Composition Analysis of Glass Chemical Composition Based on Time-Series and Clustering Methods

by Ying Zou

Molecules 2023, 28(2), 853; https://doi.org/10.3390/molecules28020853 - 14 Jan 2023

Cited by 3 | Viewed by 1287

Abstract

The weathering of ancient glass relics has long been a concerned. Therefore, a systematic and more comprehensive mathematical model with which to correctly judge the category of ancient glass products whose chemical composition changes due to weathering should be established. This paper systematically analyzes and studies the changes in the composition of ancient glass products as a result of weathering of. We first analyze the surface weathering of glass relics and its correlation with three properties and establish a multivariable time-series model to predict the chemical-composition content before weathering. Next, we use one-way analysis of variance for subclassification and, finally, we use a principal component analysis of the rationality, and change the significance level to determine its sensitivity, for the reasonable prediction of the chemical-composition content and classification to provide a theoretical basis for improving the model. This allows the model to provide reference values, which can be used in the protection of cultural relics, historical research, and other fields. Full article

(This article belongs to the Special Issue Study of Molecules in the Light of Spectral Graph Theory)

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12 pages, 312 KiB

Open AccessArticle

Comparative Study of Planar Octahedron Molecular Structure via Eccentric Invariants

by Zheng-Qing Chu, Haidar Ali, Didar Abdulkhaleq Ali, Muhammad Nadeem, Syed Ajaz K. Kirmani and Parvez Ali

Molecules 2023, 28(2), 556; https://doi.org/10.3390/molecules28020556 - 5 Jan 2023

Cited by 1 | Viewed by 1122

Abstract

A branch of graph theory that makes use of a molecular graph is called chemical graph theory. Chemical graph theory is used to depict a chemical molecule. A graph is connected if there is an edge between every pair of vertices. A topological index is a numerical value related to the chemical structure that claims to show a relationship between chemical structure and various physicochemical attributes, chemical reactivity, or, you could say, biological activity. In this article, we examined the topological properties of a planar octahedron network of m dimensions and computed the total eccentricity, average eccentricity, Zagreb eccentricity, geometric arithmetic eccentricity, and atom bond connectivity eccentricity indices, which are used to determine the distance between the vertices of a planar octahedron network. Full article

(This article belongs to the Special Issue Study of Molecules in the Light of Spectral Graph Theory)

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17 pages, 2259 KiB

Open AccessArticle

by Muhammad Usman Ghani, Francis Joseph H. Campena, Muhammad Kashif Maqbool, Jia-Bao Liu, Sanaullah Dehraj, Murat Cancan and Fahad M. Alharbi

Molecules 2023, 28(1), 452; https://doi.org/10.3390/molecules28010452 - 3 Jan 2023

Cited by 4 | Viewed by 1487

Abstract

Entropy is a measure of a system’s molecular disorder or unpredictability since work is produced by organized molecular motion. Shannon’s entropy metric is applied to represent a random graph’s variability. Entropy is a thermodynamic function in physics that, based on the variety of possible configurations for molecules to take, describes the randomness and disorder of molecules in a given system or process. Numerous issues in the fields of mathematics, biology, chemical graph theory, organic and inorganic chemistry, and other disciplines are resolved using distance-based entropy. These applications cover quantifying molecules’ chemical and electrical structures, signal processing, structural investigations on crystals, and molecular ensembles. In this paper, we look at K-Banhatti entropies using K-Banhatti indices for

C_{6} H_{6}

embedded in different chemical networks. Our goal is to investigate the valency-based molecular invariants and K-Banhatti entropies for three chemical networks: the circumnaphthalene (

C N B_{n}

), the honeycomb (

H B_{n}

), and the pyrene (

P Y_{n}

). In order to reach conclusions, we apply the method of atom-bond partitioning based on valences, which is an application of spectral graph theory. We obtain the precise values of the first K-Banhatti entropy, the second K-Banhatti entropy, the first hyper K-Banhatti entropy, and the second hyper K-Banhatti entropy for the three chemical networks in the main results and conclusion. Full article

(This article belongs to the Special Issue Study of Molecules in the Light of Spectral Graph Theory)

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12 pages, 326 KiB

Open AccessArticle

Some Novel Results Involving Prototypical Computation of Zagreb Polynomials and Indices for SiO₄ Embedded in a Chain of Silicates

by El Sayed M. Tag El Din, Faisal Sultan, Muhammad Usman Ghani, Jia-Bao Liu, Sanaullah Dehraj, Murat Cancan, Fahad M. Alharbi and Abdullah Alhushaybari

Molecules 2023, 28(1), 201; https://doi.org/10.3390/molecules28010201 - 26 Dec 2022

Cited by 7 | Viewed by 1182

Abstract

A topological index as a graph parameter was obtained mathematically from the graph’s topological structure. These indices are useful for measuring the various chemical characteristics of chemical compounds in the chemical graph theory. The number of atoms that surround an atom in the molecular structure of a chemical compound determines its valency. A significant number of valency-based molecular invariants have been proposed, which connect various physicochemical aspects of chemical compounds, such as vapour pressure, stability, elastic energy, and numerous others. Molecules are linked with numerical values in a molecular network, and topological indices are a term for these values. In theoretical chemistry, topological indices are frequently used to simulate the physicochemical characteristics of chemical molecules. Zagreb indices are commonly employed by mathematicians to determine the strain energy, melting point, boiling temperature, distortion, and stability of a chemical compound. The purpose of this study is to look at valency-based molecular invariants for

S i O_{4}

embedded in a silicate chain under various conditions. To obtain the outcomes, the approach of atom–bond partitioning according to atom valences was applied by using the application of spectral graph theory, and we obtained different tables of atom—bond partitions of

S i O_{4}

. We obtained exact values of valency-based molecular invariants, notably the first Zagreb, the second Zagreb, the hyper-Zagreb, the modified Zagreb, the enhanced Zagreb, and the redefined Zagreb (first, second, and third). We also provide a graphical depiction of the results that explains the reliance of topological indices on the specified polynomial structure parameters. Full article

(This article belongs to the Special Issue Study of Molecules in the Light of Spectral Graph Theory)

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31 pages, 9539 KiB

Open AccessArticle

Neighbourhood Sum Degree-Based Indices and Entropy Measures for Certain Family of Graphene Molecules

by Jun Yang, Julietraja Konsalraj and Arul Amirtha Raja S.

Molecules 2023, 28(1), 168; https://doi.org/10.3390/molecules28010168 - 25 Dec 2022

Cited by 13 | Viewed by 1696

Abstract

A topological index (TI) is a real number that defines the relationship between a chemical structure and its properties and remains invariant under graph isomorphism. TIs defined for chemical structures are capable of predicting physical properties, chemical reactivity and biological activity. Several kinds of TIs have been defined and studied for different molecular structures. Graphene is the thinnest material known to man and is also extremely strong while being a good conductor of heat and electricity. With such unique features, graphene and its derivatives have found commercial uses and have also fascinated theoretical chemists. In this article, the neighbourhood sum degree-based M-polynomial and entropy measures have been computed for graphene, graphyne and graphdiyne structures. The proper analytical expressions for these indices are derived. The obtained results will enable theoretical chemists to study these exciting structures further from a structural perspective. Full article

(This article belongs to the Special Issue Study of Molecules in the Light of Spectral Graph Theory)

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13 pages, 3202 KiB

Open AccessArticle

Cascade Forest-Based Model for Prediction of RNA Velocity

by Zhiliang Zeng, Shouwei Zhao, Yu Peng, Xiang Hu and Zhixiang Yin

Molecules 2022, 27(22), 7873; https://doi.org/10.3390/molecules27227873 - 15 Nov 2022

Cited by 1 | Viewed by 1416

Abstract

In recent years, single-cell RNA sequencing technology (scRNA-seq) has developed rapidly and has been widely used in biological and medical research, such as in expression heterogeneity and transcriptome dynamics of single cells. The investigation of RNA velocity is a new topic in the study of cellular dynamics using single-cell RNA sequencing data. It can recover directional dynamic information from single-cell transcriptomics by linking measurements to the underlying dynamics of gene expression. Predicting the RNA velocity vector of each cell based on its gene expression data and formulating RNA velocity prediction as a classification problem is a new research direction. In this paper, we develop a cascade forest model to predict RNA velocity. Compared with other popular ensemble classifiers, such as XGBoost, RandomForest, LightGBM, NGBoost, and TabNet, it performs better in predicting RNA velocity. This paper provides guidance for researchers in selecting and applying appropriate classification tools in their analytical work and suggests some possible directions for future improvement of classification tools. Full article

(This article belongs to the Special Issue Study of Molecules in the Light of Spectral Graph Theory)

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14 pages, 322 KiB

Open AccessArticle

Connecting SiO₄ in Silicate and Silicate Chain Networks to Compute Kulli Temperature Indices

by Ying-Fang Zhang, Muhammad Usman Ghani, Faisal Sultan, Mustafa Inc and Murat Cancan

Molecules 2022, 27(21), 7533; https://doi.org/10.3390/molecules27217533 - 3 Nov 2022

Cited by 11 | Viewed by 1607

Abstract

A topological index is a numerical parameter that is derived mathematically from a graph structure. In chemical graph theory, these indices are used to quantify the chemical properties of chemical compounds. We compute the first and second temperature, hyper temperature indices, the sum connectivity temperature index, the product connectivity temperature index, the reciprocal product connectivity temperature index and the F temperature index of a molecular graph silicate network and silicate chain network. Furthermore, a QSPR study of the key topological indices is provided, and it is demonstrated that these topological indices are substantially linked with the physicochemical features of COVID-19 medicines. This theoretical method to find the temperature indices may help chemists and others in the pharmaceutical industry forecast the properties of silicate networks and silicate chain networks before trying. Full article

(This article belongs to the Special Issue Study of Molecules in the Light of Spectral Graph Theory)

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19 pages, 1474 KiB

Open AccessArticle

A Paradigmatic Approach to Find the Valency-Based K-Banhatti and Redefined Zagreb Entropy for Niobium Oxide and a Metal–Organic Framework

by Muhammad Usman Ghani, Faisal Sultan, El Sayed M. Tag El Din, Abdul Rauf Khan, Jia-Bao Liu and Murat Cancan

Molecules 2022, 27(20), 6975; https://doi.org/10.3390/molecules27206975 - 17 Oct 2022

Cited by 16 | Viewed by 1711

Abstract

Entropy is a thermodynamic function in chemistry that reflects the randomness and disorder of molecules in a particular system or process based on the number of alternative configurations accessible to them. Distance-based entropy is used to solve a variety of difficulties in biology, chemical graph theory, organic and inorganic chemistry, and other fields. In this article, the characterization of the crystal structure of niobium oxide and a metal–organic framework is investigated. We also use the information function to compute entropies by building these structures with degree-based indices including the K-Banhatti indices, the first redefined Zagreb index, the second redefined Zagreb index, the third redefined Zagreb index, and the atom-bond sum connectivity index. Full article

(This article belongs to the Special Issue Study of Molecules in the Light of Spectral Graph Theory)

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14 pages, 286 KiB

Open AccessArticle

The Expected Values for the Gutman Index and Schultz Index in the Random Regular Polygonal Chains

by Xinmei Liu and Qian Zhan

Molecules 2022, 27(20), 6838; https://doi.org/10.3390/molecules27206838 - 12 Oct 2022

Cited by 1 | Viewed by 1166

Abstract

Two famous topological indices, the Gutman index and Schultz index, are studied in this article. We mainly calculate the exact analytical formulae for the expected values of the Gutman index and Schultz index of a random regular polygonal chain with n regular polygons. Moreover, we determine the average values and the extremal values of the indices in regard to the set of all these regular polygonal chains. Full article

(This article belongs to the Special Issue Study of Molecules in the Light of Spectral Graph Theory)

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20 pages, 1141 KiB

Open AccessArticle

On Some Topological Indices Defined via the Modified Sombor Matrix

by Xuewu Zuo, Bilal Ahmad Rather, Muhammad Imran and Akbar Ali

Molecules 2022, 27(19), 6772; https://doi.org/10.3390/molecules27196772 - 10 Oct 2022

Cited by 3 | Viewed by 2013

Abstract

Let G be a simple graph with the vertex set

V = {v_{1}, \dots, v_{n}}

and denote by

d_{v_{i}}

the degree of the vertex

v_{i}

. The modified Sombor index of G is the [...] Read more.

Let G be a simple graph with the vertex set

V = {v_{1}, \dots, v_{n}}

and denote by

d_{v_{i}}

the degree of the vertex

v_{i}

. The modified Sombor index of G is the addition of the numbers

{(d_{v_{i}}^{2} + d_{v_{j}}^{2})}^{- 1 / 2}

over all of the edges

v_{i} v_{j}

of G. The modified Sombor matrix

A_{M S} (G)

of G is the n by n matrix such that its

(i, j)

-entry is equal to

{(d_{v_{i}}^{2} + d_{v_{j}}^{2})}^{- 1 / 2}

when

v_{i}

and

v_{j}

are adjacent and 0 otherwise. The modified Sombor spectral radius of G is the largest number among all of the eigenvalues of

A_{M S} (G)

. The sum of the absolute eigenvalues of

A_{M S} (G)

is known as the modified Sombor energy of G. Two graphs with the same modified Sombor energy are referred to as modified Sombor equienergetic graphs. In this article, several bounds for the modified Sombor index, the modified Sombor spectral radius, and the modified Sombor energy are found, and the corresponding extremal graphs are characterized. By using computer programs (Mathematica and AutographiX), it is found that there exists only one pair of the modified Sombor equienergetic chemical graphs of an order of at most seven. It is proven that the modified Sombor energy of every regular, complete multipartite graph is

\sqrt{2}

; this result gives a large class of the modified Sombor equienergetic graphs. The (linear, logarithmic, and quadratic) regression analyses of the modified Sombor index and the modified Sombor energy together with their classical versions are also performed for the boiling points of the chemical graphs of an order of at most seven. Full article

(This article belongs to the Special Issue Study of Molecules in the Light of Spectral Graph Theory)

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15 pages, 454 KiB

Open AccessArticle

On Topological Properties for Benzenoid Planar Octahedron Networks

by Jia-Bao Liu, Haidar Ali, Qurat Ul Ain, Parvez Ali and Syed Ajaz K. Kirmani

Molecules 2022, 27(19), 6366; https://doi.org/10.3390/molecules27196366 - 27 Sep 2022

Cited by 3 | Viewed by 1347

Abstract

Chemical descriptors are numeric numbers that capture the whole graph structure and comprise a basic chemical structure. As a topological descriptor, it correlates with certain physical aspects in addition to its chemical representation of underlying chemical substances. In the modelling and design of any chemical network, the graph is important. A number of chemical indices have been developed in theoretical chemistry, including the Wiener index, the Randić index, and many others. In this paper, we look at the benzenoid networks and calculate the exact topological indices based on the degrees of the end vertices. Full article

(This article belongs to the Special Issue Study of Molecules in the Light of Spectral Graph Theory)

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19 pages, 293 KiB

Open AccessArticle

Hosoya Polynomials of Power Graphs of Certain Finite Groups

by Bilal Ahmad Rather, Fawad Ali, Suliman Alsaeed and Muhammad Naeem

Molecules 2022, 27(18), 6081; https://doi.org/10.3390/molecules27186081 - 18 Sep 2022

Cited by 6 | Viewed by 1387

Abstract

Assume that

G

is a finite group. The power graph

P (G)

G

is a graph in which

G

is its node set, where two different elements are connected by an edge whenever one of them is a power of [...] Read more.

Assume that

G

is a finite group. The power graph

P (G)

G

is a graph in which

G

is its node set, where two different elements are connected by an edge whenever one of them is a power of the other. A topological index is a number generated from a molecular structure that indicates important structural properties of the proposed molecule. Indeed, it is a numerical quantity connected with the chemical composition that is used to correlate chemical structures with various physical characteristics, chemical reactivity, and biological activity. This information is important for identifying well-known chemical descriptors based on distance dependence. In this paper, we study Hosoya properties, such as the Hosoya polynomial and the reciprocal status Hosoya polynomial of power graphs of various finite cyclic and non-cyclic groups of order

p q

and

p q r

, where

p, q

and

r (p \geq q \geq r)

are prime numbers. Full article

(This article belongs to the Special Issue Study of Molecules in the Light of Spectral Graph Theory)

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15 pages, 351 KiB

Open AccessArticle

Certain Topological Indices of Non-Commuting Graphs for Finite Non-Abelian Groups

by Fawad Ali, Bilal Ahmad Rather, Muhammad Sarfraz, Asad Ullah, Nahid Fatima and Wali Khan Mashwani

Molecules 2022, 27(18), 6053; https://doi.org/10.3390/molecules27186053 - 16 Sep 2022

Cited by 5 | Viewed by 1240

Abstract

A topological index is a number derived from a molecular structure (i.e., a graph) that represents the fundamental structural characteristics of a suggested molecule. Various topological indices, including the atom-bond connectivity index, the geometric–arithmetic index, and the Randić index, can be utilized to [...] Read more.

Γ_{G}

of a finite group

G

is a graph where non-central elements of

G

are its vertex set, while two different elements are edge connected when they do not commute in

G

. In this article, we investigate several topological properties of non-commuting graphs of finite groups, such as the Harary index, the harmonic index, the Randić index, reciprocal Wiener index, atomic-bond connectivity index, and the geometric–arithmetic index. In addition, we analyze the Hosoya characteristics, such as the Hosoya polynomial and the reciprocal status Hosoya polynomial of the non-commuting graphs over finite subgroups of

SL (2, C)

. We then calculate the Hosoya index for non-commuting graphs of binary dihedral groups. Full article

(This article belongs to the Special Issue Study of Molecules in the Light of Spectral Graph Theory)

12 pages, 288 KiB

Open AccessArticle

Enumeration of the Multiplicative Degree-Kirchhoff Index in the Random Polygonal Chains

by Wanlin Zhu and Xianya Geng

Molecules 2022, 27(17), 5669; https://doi.org/10.3390/molecules27175669 - 2 Sep 2022

Cited by 4 | Viewed by 4629

Abstract

Multiplicative degree-Kirchhoff index is a very interesting topological index. In this article, we compute analytical expression for the expected value of the Multiplicative degree-Kirchhoff index in a random polygonal. Based on the result above, we also get the Multiplicative degree-Kirchhoff index of all [...] Read more.

(This article belongs to the Special Issue Study of Molecules in the Light of Spectral Graph Theory)

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Review

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20 pages, 1251 KiB

Open AccessReview

Flavonoid Components, Distribution, and Biological Activities in Taxus: A review

by Qiang Wei, Qi-Zhao Li and Rui-Lin Wang

Molecules 2023, 28(4), 1713; https://doi.org/10.3390/molecules28041713 - 10 Feb 2023

Cited by 9 | Viewed by 1955

Abstract

Taxus, also known as “gold in plants” because of the famous agents with emphases on Taxol and Docetaxel, is a genus of the family Taxaceae, distributed almost around the world. The plants hold an important place in traditional medicine in China, and its products are used for treating treat dysuria, swelling and pain, diabetes, and irregular menstruation in women. In order to make a further study and better application of Taxus plants for the future, cited references from between 1958 and 2022 were collected from the Web of Science, the China National Knowledge Internet (CNKI), SciFinder, and Google Scholar, and the chemical structures, distribution, and bioactivity of flavonoids identified from Taxus samples were summed up in the research. So far, 59 flavonoids in total with different skeletons were identified from Taxus plants, presenting special characteristics of compound distribution. These compounds have been reported to display significant antibacterial, antiaging, anti-Alzheimer’s, antidiabetes, anticancer, antidepressant, antileishmaniasis, anti-inflammatory, antinociceptive and antiallergic, antivirus, antilipase, neuronal protective, and hepatic-protective activities, as well as promotion of melanogenesis. Flavonoids represent a good example of the utilization of the Taxus species. In the future, further pharmacological and clinical experiments for flavonoids could be accomplished to promote the preparation of relative drugs. Full article

(This article belongs to the Special Issue Study of Molecules in the Light of Spectral Graph Theory)

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