Network-Based Modeling of the Molecular Topology of Fuchsine Acid Dye with Respect to Some Irregular Molecular Descriptors

Ullah, Asad; Shamsudin,; Zaman, Shahid; Hamraz, Anila; Saeedi, Ghulamullah

doi:10.1155/2022/8131276

Cited by 35 publications

(15 citation statements)

References 25 publications

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“…The expressions for number of spanning trees and Kirchhoff index for different networks, including cycles [23], linear polyomino chains [24], linear crossed octagonal chains [25], circulant graphs [26] , linear crossed hexagonal chains [27], cylinder phenylene chains [28], linear hexagonal chains [29], ladder graphs [30], ladderlike chains [31], and linear phenylenes [32] were calculated by different researchers. For more related results, the readers can see [33][34][35][36][37][38].…”

Section: Construction Of K 4 Ring and Formulation Of Random Walk Para...mentioning

confidence: 99%

Spectral techniques and mathematical aspects of K ₄ chain graph

Yan

Kosar²,

Aslam

et al. 2023

Phys. Scr.

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The resistance distance between any two vertices of a connected graph is defined as the net effective resistance between them. An electrical network can be constructed from a graph by replacing each edge with a unit resistor. Resistance distances are computed by methods of the theory of resistive electrical networks (based on Ohm's and Kirchhoff's laws). The standard method to compute resistance distance is via the Moore-Penrose generalized inverse of the Laplacian matrix of the underlying graph G. In this article, we used the electric network approach and the combinatorial approach, to derive the exact expression for resistance distances between any two vertices of the Kn 4 ring model. By employing a recursive connection, firstly we determined all the eigenvalues and their multiplicities in relation to the corresponding Laplacian and normalised matrices. Secondly, we obtained the Kirchhoff index and multiplicative degree Kirchhoff index for Kn 4. Finally, we calculated the mean first passage time and Kemeny constant of Kn 4. Our computed results provide a comprehensive approach for exploring random walks on complex networks, especially biased random walks, which may also help to better understand and tackle some practical problems such as search and routing on networks.

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Section: Construction Of K 4 Ring and Formulation Of Random Walk Para...mentioning

confidence: 99%

Spectral techniques and mathematical aspects of K ₄ chain graph

Yan

Kosar²,

Aslam

et al. 2023

Phys. Scr.

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“…Vertices of graphs represent atoms, and edges represent the bonds between atoms. Computing and the applications of topological indices have recently become active research areas. − In this work, we use several topological indices of various antischizophrenic drugs to determine their physical properties and chemical reactivity. QSPR models are built by using topological indices and linear regression for drugs used for the treatment of schizophrenia.…”

Section: Introductionmentioning

confidence: 99%

QSPR Analysis of Drugs for Treatment of Schizophrenia Using Topological Indices

Zhang,

Saif,

Idrees

et al. 2023

ACS Omega

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Schizophrenia is a chronic psychotic disorder characterized primarily by cognitive deficits. Drugs and therapies are helpful in managing the symptoms, mostly with long-term compliance. There is a pressing need to design more efficient drugs with fewer adverse effects. Solubility, metabolic stability, toxicity, permeability, and transporter effects are important parameters in the efficacy of drug design, which in turn depend upon different physical and chemical characteristics of drugs. In recent years, there has been growing interest in developing computational tools for the discovery and development of drugs for schizophrenia. Some of these methods use machine learning algorithms to predict the efficacy and side effects of the potential drugs. Other studies have used computer simulations to understand the molecular mechanisms underlying the disease and identify new targets for drug development. Topological indices are numeric quantities linked to the chemical structure of drugs and predict the properties, reactivity, and stability of drugs through the quantitative structure−property relationship (QSPR). This work is aimed at using statistical techniques to link QSPR correlating properties with connectivity indices using linear regression. The QSPR model gives quite a better estimation of the properties of drugs, such as melting point, boiling point, enthalpy, flash point, molar refractivity, refractive index, complexity, molecular weight, and refractivity. Results are validated by comparing actual values to estimated values for the drugs.

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“…Graph theory is a fundamental branch of mathematics that studies the properties and relationships of graphs, which consist of vertices (nodes) connected by edges [1,2]. Graph theory, pioneered by Leonhard Euler in the 18th century, has emerged as a vital area of study in mathematics and computer science [3][4][5][6]. It provides a framework for understanding and solving problems related to networks, relationships, and structures.…”

Section: Introductionmentioning

confidence: 99%

The number of spanning trees in a k5 chain graph

Kosar,

Zaman,

Ali

et al. 2023

Phys. Scr.

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Spanning trees (ST) have numerous applications in various ﬁelds, including computer science, graph theory, network design, and optimization. ST uses in designing eﬃcient network topologies. In computer networks, a ST ensures that all nodes are connected while avoiding loops and redundant connections. This helps in minimizing network congestion and ensuring reliable communication. In routing protocols the ST’s play a crucial role such as the Spanning Tree Protocol (STP) and Rapid Spanning Tree Protocol (RSTP). These protocols are used to prevent network loops and establish a loop-free topology for eﬃcient packet forwarding.

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Network-Based Modeling of the Molecular Topology of Fuchsine Acid Dye with Respect to Some Irregular Molecular Descriptors

Cited by 35 publications

References 25 publications

Spectral techniques and mathematical aspects of K ₄ chain graph

Spectral techniques and mathematical aspects of K ₄ chain graph

QSPR Analysis of Drugs for Treatment of Schizophrenia Using Topological Indices

The number of spanning trees in a k5 chain graph

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Network-Based Modeling of the Molecular Topology of Fuchsine Acid Dye with Respect to Some Irregular Molecular Descriptors

Cited by 35 publications

References 25 publications

Spectral techniques and mathematical aspects of K 4 chain graph

Spectral techniques and mathematical aspects of K 4 chain graph

QSPR Analysis of Drugs for Treatment of Schizophrenia Using Topological Indices

The number of spanning trees in a k5 chain graph

Contact Info

Product

Resources

About

Spectral techniques and mathematical aspects of K ₄ chain graph

Spectral techniques and mathematical aspects of K ₄ chain graph