Topological Descriptors on Some Families of Graphs

Ahmad, Iftikhar; Chaudhry, Maqbool Ahmad; Hussain, Muhammad; Mahmood, Tariq

doi:10.1155/2021/6018893

Cited by 4 publications

(4 citation statements)

References 11 publications

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“…Wiener polynomial and Wiener index for subdivision graph of friendship and bifriendship graphs and line graph subdivision graph of friendship and bifriendship graphs can be applied to many practical graphs [27,22,25,11,24,35,15,36,32,18] such as Dutch windmill graph, paracactus chain graphs, Oxide network and chain silicate, molecular structure of Ethane, molecular graph of Ethane and Para-line graph of Ethane, Polyphony Chains, dicoronylene, biphenylene, and V-Phenylenic nanosheet.…”

Section: Applicationsmentioning

confidence: 99%

Computation of wiener polynomial and index of line subdivision friendship and line subdivision bifriendship graphs using matlab program

Al-Rumaima,

Alameri,

Al-Sharafi

et al. 2024

Proyecciones (Antofagasta)

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A topological index is a branch of chemical graph theory that is vital to analyzing the physio-chemical characteristics of chemical compound structures divided into a degree-based molecular structure such as Zagreb indices, a distance-based molecular structure such as Wiener index, and a mixed such as Gutman index. In this paper, some definitions, results, and examples of Wiener polynomial and index for subdivision graph of friendship, bifriendship graphs, line subdivision graph of friendship, and bifriendship graphs were introduced. Moreover, we used the MATLAB program to calculate the Wiener polynomial and index of these graphs and refer to some applications.

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Section: Applicationsmentioning

confidence: 99%

Computation of wiener polynomial and index of line subdivision friendship and line subdivision bifriendship graphs using matlab program

Al-Rumaima,

Alameri,

Al-Sharafi

et al. 2024

Proyecciones (Antofagasta)

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“…The main goal of "quantitative structure-property relationships" and "quantitative structure-activity relationships" is to examine the connections between molecular structures and the properties or activities they have in different areas like medicine, pharmaceuticals, medical research, rational drug design, and experimental science [6]. The researchers analyzed different behaviors of chemical compounds in quantitative structure-property relationships [7,8] through topological indices. Kirmani et al [9] examined the different topological variants and the physicochemical attributes of drugs employed in treating coronavirus.…”

Section: Introductionmentioning

confidence: 99%

On K-Banhatti, Revan Indices and Entropy Measures of MgO(111) Nanosheets via Linear Regression

Almalki,

Tabassum

2024

Mathematics

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The structure and topology of chemical compounds can be determined using chemical graph theory. Using topological indices, we may uncover much about connectivity, complexity, and other important aspects of molecules. Numerous research investigations have been conducted on the K-Banhatti indices and entropy measurements in various fields, including the study of natural polymers, nanotubes, and catalysts. At the same time, the Shannon entropy of a graph is widely used in network science. It is employed in evaluating several networks, including social networks, neural networks, and transportation systems. The Shannon entropy enables the analysis of a network’s topology and structure, facilitating the identification of significant nodes or structures that substantially impact network operation and stability. In the past decade, there has been a considerable focus on investigating a range of nanostructures, such as nanosheets and nanoparticles, in both experimental and theoretical domains. As a very effective catalyst and inert substrate, the MgO nanostructure has received a lot of interest. The primary objective of this research is to study different indices and employ them to look at entropy measures of magnesium oxide(111) nanosheets over a wide range of p values, including p=1,2,3,⋯,j. Additionally, we conducted a linear regression analysis to establish the correlation between indices and entropies.

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“…The study has implications in the fields of computer science, physics, electronics, chemistry, mathematics, and bioinformatics for modeling purposes of networks of the PV system, intelligent systems, puzzle games and chemical compounds [15]. KBSO, CQIs, ISOs and dharwad invariants with their reduced forms allow us to accumulate information about algebraic structures and mathematically predict hidden properties of various structures such as Sudoku networks [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Intelligent Systems and Photovoltaic Cells Empowered Topologically by Sudoku Networks

Hamid¹,

Iqbal²,

Ashraf³

et al. 2023

Computers, Materials &Amp; Continua

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A graph invariant is a number that can be easily and uniquely calculated through a graph. Recently, part of mathematical graph invariants has been portrayed and utilized for relationship examination. Nevertheless, no reliable appraisal has been embraced to pick, how much these invariants are associated with a network graph in interconnection networks of various fields of computer science, physics, and chemistry. In this paper, the study talks about sudoku networks will be networks of fractal nature having some applications in computer science like sudoku puzzle game, intelligent systems, Local area network (LAN) development and parallel processors interconnections, music composition creation, physics like power generation interconnections, Photovoltaic (PV) cells and chemistry, synthesis of chemical compounds. These networks are generally utilized in disorder, fractals, recursive groupings, and complex frameworks. Our outcomes are the normal speculations of currently accessible outcomes for specific classes of such kinds of networks of two unmistakable sorts with two invariants K-banhatti sombor (KBSO) invariants, Irregularity sombor (ISO) index, Contraharmonic-quadratic invariants (CQIs) and dharwad invariants with their reduced forms. The study solved the Sudoku network used in mentioned systems to improve the performance and find irregularities present in them. The calculated outcomes can be utilized for the modeling, scalability, introduction of new architectures of sudoku puzzle games, intelligent systems, PV cells, interconnection networks, chemical compounds, and extremely huge scope in very large-scale integrated circuits (VLSI) of processors.

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Topological Descriptors on Some Families of Graphs

Cited by 4 publications

References 11 publications

Computation of wiener polynomial and index of line subdivision friendship and line subdivision bifriendship graphs using matlab program

Computation of wiener polynomial and index of line subdivision friendship and line subdivision bifriendship graphs using matlab program

On K-Banhatti, Revan Indices and Entropy Measures of MgO(111) Nanosheets via Linear Regression

Intelligent Systems and Photovoltaic Cells Empowered Topologically by Sudoku Networks

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