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Article
Mathematics, Applied
Shahid Zaman et al.
Summary: This paper investigates the random walks of octagonal cell network by using the Laplacian spectrum method. The mean first passage time (τ) and Kemeny's constant (Ω) between nodes are obtained. The mean first passage time (τ) is explicitly studied in terms of the eigenvalues of a Laplacian matrix, while Kemeny's constant (Ω) is introduced to measure node strength and determine the scaling of the random walks. An explicit expression of Kemeny's constant and mean first passage time for octagonal cell network is provided based on Laplacian eigenvalues and the correlation among roots of characteristic polynomial. Comparative studies are also performed for τ and Ω based on the achieved results. This work also delivers an inclusive approach for exploring random walks of networks, particularly biased random walks, which can help better understand and tackle practical problems such as search and routing on networks.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Physics, Multidisciplinary
Asad Ullah et al.
Summary: Mathematical chemistry uses mathematics to solve chemistry problems. This paper calculates and derives closed formulas for the first and second Zagreb connection indices of triangular chain structures. By using these formulas and obtained numerical results, the physicochemical properties of these structures can be easily investigated.
Article
Computer Science, Information Systems
Xiaodong Yu et al.
Summary: Recent advances in graph-structured learning have shown promising results in graph classification, but scaling them on large graphs with millions of nodes and edges remains a challenge due to their high temporal complexity. This paper establishes an explicit closed-form formula for the global mean-first-passage time (GMFPT) in hexagonal models through the decomposition theorem of Laplacian polynomial and characteristic polynomial. Our method uses GMFPT to estimate transport speed for random walks on complex networks, and through matrix analysis, we demonstrate that obtaining GMFPT via spectrums allows for easy calculation in large networks.
Article
Biochemistry & Molecular Biology
Asad Ullah et al.
Summary: Quantitative structure-activity relationship (QSAR) is a method that correlates the biological structural features (topological indices) with pharmacological activity. Topological indices are numerical functions used to predict the growth rate of microorganisms in biological networks. Theoretical assessment of microorganisms helps in vaccine design and discovery by understanding their mechanism of actions. This article investigates the biological properties of two important biological networks (hypertree and its corona product) by obtaining novel topological features and deriving closed formulas for them.
JOURNAL OF BIOMOLECULAR STRUCTURE & DYNAMICS
(2023)
Article
Physics, Multidisciplinary
Tao Yan et al.
Summary: In this article, the exact expression for resistance distances between any two vertices of the K-4(n) ring model was derived using the electric network approach and the combinatorial approach. The Kirchhoff index, multiplicative degree Kirchhoff index, mean first passage time, and Kemeny constant of K-4(n) were also calculated. These computed results provide a comprehensive approach for exploring random walks on complex networks and may help to solve practical problems such as search and routing on networks.
Article
Multidisciplinary Sciences
Shahid Zaman et al.
Summary: Metal-Organic Networks (MONs) are crystalline porous solids made of metal ions and organic ligands, with wide-ranging applications in gas storage, purification, drug delivery, separation, catalysis, and sensing. The study focuses on calculating and analyzing various molecular descriptors for two separate MONs, which play a crucial role in theoretical and ecological chemistry, as well as medicine.
SCIENTIFIC REPORTS
(2023)
Article
Chemistry, Organic
Xiujun Zhang et al.
Summary: Nanostructures are important and extensively studied compounds in chemical science. The computation and study of topological indices for these structures are crucial in the field of nanotechnology. This paper computes topological indices based on ev-degree and ve-degree for carbon nanosheets, providing a foundation for the study of structure-property relationships in carbon nanotube compounds.
POLYCYCLIC AROMATIC COMPOUNDS
(2022)
Article
Mathematics
Shahid Zaman et al.
Summary: This paper focuses on the relations between the inertia indices of a T-gain graph and the inertia indices of its underlying graph. It provides sharp lower and upper bounds on the inertia indices and characterizes the corresponding extremal T-gain graphs and signed graphs.
LINEAR & MULTILINEAR ALGEBRA
(2022)
Article
Biochemical Research Methods
Xiujun Zhang et al.
Summary: Cerium oxide nanoparticles are widely used as catalysts in industry, leading to their significant presence in water systems. This study focuses on analyzing the crystal structure of Ceria Oxide and calculating the Heat of Formation and Entropy using degree-based topological indices. Various topological indices were computed and discussed in relation to the physical properties of the cuprite CeO2 nanocrystal, showing potential for nanoceria engineering.
COMBINATORIAL CHEMISTRY & HIGH THROUGHPUT SCREENING
(2022)
Article
Mathematics, Applied
Shahid Zaman
Summary: This paper studies the eigenvalues, Laplacian matrix, and Kirchhoff index of rounded networks. By using the decomposition theorem of Laplacian polynomial, explicit formulas are obtained and applied to the number of spanning trees and mean-first passage time. Additionally, it is shown that the Kirchhoff index of N-n is approximately 1/3 of its Wiener index.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2022)
Article
Engineering, Multidisciplinary
Junhao Peng et al.
Summary: This study focuses on improving the trapping efficiency in regular branched networks by analyzing biased random walks on a family of weighted Cayley trees. By calculating quantities for measuring the trapping efficiency and optimizing with respect to parameter r, the highest trapping efficiency can be achieved in different scenarios.
IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Asad Ullah et al.
Summary: The recent discovery of various forms of carbon nanostructures has inspired researchers due to their potential uses in various fields. Molecular descriptors play an important role in mathematical chemistry, allowing for the analysis of physicochemical properties of molecules and providing insights for the investigation of quantitative structure-property relationships and quantitative structure-activity relationships.
AIN SHAMS ENGINEERING JOURNAL
(2022)
Article
Mathematics
Ali Al Khabyah et al.
Summary: This paper investigates the minimum transmission in two-mode networks by analyzing the parameters of connected nodes and paths in bipartite networks. Furthermore, the regression model of boiling point in benzenoid hydrocarbons is studied, and the correlation between different eccentricity indices and boiling point is compared.
Article
Mathematics
Tengjie Chen et al.
Summary: The paper introduces the generation and iteration methods of the n-polygon graph and presents a method for calculating the eigenvalues of the normalized Laplacian matrix. Furthermore, by exploring the relationships between the graph structure and the normalized Laplacian spectrum, it calculates important graph properties and obtains exact results.
LINEAR & MULTILINEAR ALGEBRA
(2022)
Article
Chemistry, Multidisciplinary
Asad Ullah et al.
Summary: This article investigates and predicts the complex molecular topology of fuchsine acid and derives closed formulae for important molecular descriptors. The study aims to shed light on the effectiveness of these descriptors for QSAR and QSPR analyses.
JOURNAL OF CHEMISTRY
(2022)
Article
Biochemistry & Molecular Biology
Asad Ullah et al.
Summary: This article investigates the chemical structure of Naphtalenic nanosheet as a chemical network by using some important degree-based topological indices. However, the computation of topological indices for the line graph of subdivision graph of H-Naphtalenic nanosheet has not been discussed so far, which may open new perspectives for a more accurate and reliable topological characterization of this nanosheet.
JOURNAL OF MOLECULAR MODELING
(2022)
Article
Mathematics
Shahid Zaman et al.
Summary: Chemical graph theory is used to model the physical and biological properties of chemical compounds, and the geometric structure of these compounds can be modeled using topological indices derived from graph theory. In this study, novel topological indices were computed for a Sudoku nanosheet, and formulas derived from these indices were used to investigate the physical and chemical properties of the nanosheet. The results showed that these computed indices have the best correlation with acentric factor and entropy.
JOURNAL OF MATHEMATICS
(2022)
Article
Physics, Multidisciplinary
Silvia Bartolucci et al.
Summary: In this research, an approximate formula for the Mean First Passage Time of a random walker on a directed and weighted network is derived, without the need for matrix inversion and using transition probabilities as input. The formula's accuracy depends on the spectral gap of the reduced transition matrix.
Article
Physics, Multidisciplinary
Xiaomin Wang et al.
Summary: In this paper, we generated a scale-free network using a rectangle operation and studied its topological structures, as well as characteristic quantities related to the network. These characteristic quantities can be used to evaluate network properties and have significant applications in science and engineering.
FRONTIERS IN PHYSICS
(2021)
Article
Management
Joost Berkhout et al.
OPERATIONS RESEARCH
(2019)
Article
Computer Science, Information Systems
Yibin Sheng et al.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2019)
Editorial Material
Chemistry, Physical
Frank Noe et al.
JOURNAL OF CHEMICAL PHYSICS
(2019)
Article
Chemistry, Multidisciplinary
Hai-Ling Zhang et al.
JOURNAL OF CHEMISTRY
(2019)
Article
Engineering, Multidisciplinary
Yi Qi et al.
IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING
(2019)
Article
Mathematics, Applied
Shin Min Kang et al.
JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY
(2019)
Article
Chemistry, Physical
Yingui Pan et al.
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY
(2018)
Article
Multidisciplinary Sciences
Xiujun Zhang et al.
Article
Chemistry, Physical
Yan Wang et al.
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY
(2010)
Review
Biochemical Research Methods
Vijay S. Pande et al.
Article
Mathematics, Applied
Haiyan Chen et al.
DISCRETE APPLIED MATHEMATICS
(2007)
