Study on the normalized Laplacian of a penta‐graphene with applications

Li, Qishun; Zaman, Shahid; Sun, Wanting; Alam, Jawad

doi:10.1002/qua.26154

Cited by 32 publications

(13 citation statements)

References 53 publications

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“…In this paper, motivated by previous studies 19–23 and by using the Laplacian decomposition theorem, we achieved the explicit closed‐form formulations for

\Omega

and

\tau

{\triangle}_n

.…”

Section: Introductionmentioning

confidence: 99%

Kemeny's constant and global mean first passage time of random walks on octagonal cell network

Zaman¹,

Ullah

2023

Math Methods in App Sciences

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This paper investigates the random walks of octagonal cell network. By using the Laplacian spectrum method, we obtain the mean first passage time (𝜏) and Kemeny's constant (Ω) between nodes. On one hand, the mean first passage time (𝜏) is explicitly studied in terms of the eigenvalues of a Laplacian matrix. On the other hand, Kemeny's constant (Ω) is introduced to measure node strength and to determine the scaling of the random walks. We provide an explicit expression of Kemeny's constant and mean first passage time for octagonal cell network, by their Laplacian eigenvalues and the correlation among roots of characteristic polynomial. Based on the achieved results, comparative studies are also performed for 𝜏 and Ω. This work also deliver an inclusive approach for exploring random walks of networks, particularly biased random walks, which likewise support to better understand and tackle some practical problems such as search and routing on networks.

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“…In this paper, motivated by previous studies 19–23 and by using the Laplacian decomposition theorem, we achieved the explicit closed‐form formulations for

\Omega

and

\tau

{\triangle}_n

.…”

Section: Introductionmentioning

confidence: 99%

Kemeny's constant and global mean first passage time of random walks on octagonal cell network

Zaman¹,

Ullah

2023

Math Methods in App Sciences

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“…In [24], Guo and Dong, gave the energy and analytical applications of chemical graphs. Li et al [25] used some matrix techniques to obtain the eigenvalues and their multiplicity to fnd the kirchhof index. In [26], Khan et al, established someproperties and applications of toxicities.…”

Section: Introductionmentioning

confidence: 99%

Structural Analysis and Topological Characterization of Sudoku Nanosheet

Zaman¹,

Jalani²,

Ullah

et al. 2022

Journal of Mathematics

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The physical and biological properties of chemical compounds are modelled using chemical graph theory. The geometric structure of chemical compounds can be modelled using a variety of topological indices derived from graph theory. The chemical structures, physicochemical characteristics, and biological activities are predicted by the topological indices using the real numbers derived from the molecular compound. The topological index’s first use was to identify the physical characteristics of alkenes. A topological index is a molecular structure descriptor calculated from a chemical compound’s molecular graph describing its topology. When applied to a chemical compound’s molecular structure, it tells the theoretical properties. The chemical structure is studied as a graph, where elements are denoted as vertices, and chemical bonds are called edges. In this study, we have computed some novel topological indices named as modified neighborhood version of the forgotten topological index F N ∗ , the neighborhood version of the first multiplicative Zagreb M 1 ∗ , the neighborhood version of the second Zagreb index M 2 ∗ , the neighborhood version of hyper-Zagreb index HM N , the Sambor topological index SO G , and the Sambor reduced topological index SO red G for the Sudoku nanosheet and derived formulas for them. Based on the derived formulas, the numerical results of the understudy nanosheet’s physical and chemical properties are investigated. Our computed results are undoubtedly helpful in understanding the topology of the understudy nanosheet. These computed indices have the best correlation with acentric factor and entropy; therefore, they are effective in QSPRs and QSARs analysis with complete accuracy.

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“…Existing studies have demonstrated that calculations of the Laplacian eigenvalues face an enormous challenge because the eigenvalues are dominated by the network topology [9][10][11]. It is of interest to explore diverse methods to reveal the correlation between the topology and the coherence [12,13].…”

Section: Introductionmentioning

confidence: 99%

Topology design for leader-follower coherence in noisy asymmetric networks

Chen¹,

Sun²,

Wang³

2022

Phys. Scr.

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In this paper, we aim to study the effect of the leader's positions in leader-follower coherence quantified by the spectrum in noisy asymmetric networks with a set of hub nodes. In order to compare the impact of leader selection in different ways on the studied coherence, we choose a family of ring-trees networks to conveniently assign the leaders and hubs. Based on the regular network topology and matrix theories, we obtain analytical solutions for the leader-follower coherence regarding network parameters and the number of leaders. Using these expressions, we then obtain exact relations among the coherences and show that the leader's positions and network parameters have a profound impact on the coherence. More specifically, the network with one hub displays better coherence than the networks with two hubs. In addition, two adjacent and nonadjacent hubs lead to distinct performance of leader-follower consensus dynamics that depends on network parameters and assigned leaders in the ring or the tree network.

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Study on the normalized Laplacian of a penta‐graphene with applications

Cited by 32 publications

References 53 publications

Kemeny's constant and global mean first passage time of random walks on octagonal cell network

Kemeny's constant and global mean first passage time of random walks on octagonal cell network

Structural Analysis and Topological Characterization of Sudoku Nanosheet

Topology design for leader-follower coherence in noisy asymmetric networks

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