Zagreb connection topological descriptors and structural property of the triangular chain structures

Ullah, Asad; udin, Shams; Zaman, Shahid; Humraz, Anila

doi:10.1088/1402-4896/acb327

Cited by 54 publications

(30 citation statements)

References 37 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.

Self Cite

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“…We take into account the situation where both the number of rows which is denoted as n and the number of benzene rings in each row are more than 1 which is denoted as m, or when n > 1 and m > 1. In this instance, tables 1-5 provide the edge end vertex set partitions acquired from figure 1 which taken from the reference [30].…”

Section: Preliminariesmentioning

confidence: 99%

On novel topological characteristics of graphene

Ediz

2023

Phys. Scr.

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Molecular topological indices are quantitative measurements that only take into account the topology of a compound’s molecular graph, disregarding any knowledge of the atom locations or chemical connections. An allotrope of carbon called graphene is composed of a single layer of atoms set up in a hexagonal lattice nanostructure. A single layer of carbon atoms organized in a honeycomb pattern make up the two-dimensional substance known as graphene. Graphene possesses significant inherent qualities like strong strength and great thermal and electrical conductivity. It is a sustainable substance with practically countless eco-friendly applications. In this study, we calculate the R molecular topological indices, S molecular topological indices, and Van molecular topological indices of graphene structure, taking into account all conceivable combinations of the number of rows and hexagons. There are high correlations between R, S Van index values and neighbourhood-based entropy values of graphene. This shows that these new indices can be used in QSPR/QSAR studies in chemistry and physics.

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“…The zinc oxide and zinc silicate exhibit physicochemical characteristics including grafting active groups 8 , incorporating appropriate active material 9 , ion exchange 10 , creating composites using various materials 11 , modifying organic ligands, photosynthetic ligands, and improving the selectivity, sensitivity, and response times of biosensors.Yap et al 12 and Lin et al 13 presented the most current developments in precursors for a variety of nanostructures and MON-related applications, including lithium ion batteries, super capacitors, photocatalysis, electrocatalysis, and catalysts for the manufacture of fine chemicals. The field of modern chemistry can benefit from using graph theory to represent the physical and chemical characteristics of chemical compounds, such as their heats of formation and evaporation, flash points, melting points, boiling points, temperatures, pressures, densities, retention times in chromatography, tensions, and partition coefficients 14 , 15 . In order to investigate many characteristics of chemical compounds (such as the boiling point of paraffin), Wiener first developed the distance-based topological index (TI) in 1947.…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis and molecular descriptors of two novel metal–organic models with chemical applications

Zaman¹,

Jalani²,

Ullah

et al. 2023

Sci Rep

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Metal–Organic Networks (MONs) are made by chemical molecules that contain metal ions and organic ligands. A crystalline porous solid called Metal–Organic Networks (MONs) is made up of a $$3D$$ 3 D metal network of ions held in place by a multidentate ligand. (MONs) can be used for gas storage, purification drug delivery, gas separation, catalysis, and sensing applications. There is enormous potential for effective integration and research of MONs in diverse applications. Molecular descriptors are arithmetic measures that reveal a chemical substance's physical and chemical characteristics in its foundational network in a natural relationship. They demonstrate an important role in theoretical and ecological chemistry, and in the field of medicine. In this research, we calculated various recently discovered molecular descriptors viz. the modified version of second zagreb index, harmonic index, reciprocal randic index, modified version of forgotten topological index, redefined first zagreb topological index, redefined second zagreb topological index and redefined third zagreb topological index for two separate metal–organic networks. The numerical and graphical comparative analysis of these considered molecular descriptors are also performed.

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Zagreb connection topological descriptors and structural property of the triangular chain structures

Cited by 54 publications

References 37 publications

Spectral techniques and mathematical aspects of K ₄ chain graph

Spectral techniques and mathematical aspects of K ₄ chain graph

On novel topological characteristics of graphene

Mathematical analysis and molecular descriptors of two novel metal–organic models with chemical applications

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Zagreb connection topological descriptors and structural property of the triangular chain structures

Cited by 54 publications

References 37 publications

Spectral techniques and mathematical aspects of K 4 chain graph

Spectral techniques and mathematical aspects of K 4 chain graph

On novel topological characteristics of graphene

Mathematical analysis and molecular descriptors of two novel metal–organic models with chemical applications

Contact Info

Product

Resources

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Spectral techniques and mathematical aspects of K ₄ chain graph

Spectral techniques and mathematical aspects of K ₄ chain graph