Dominating Topological Analysis and Comparison of the Cellular Neural Network

Ejaz, Farukh; Hussain, Muhammad Tahir; Almohamedh, Hamad; Alhamed, Khalid; Alabdan, Rana; Almotairi, Sultan

doi:10.1155/2021/6613433

Cited by 6 publications

(3 citation statements)

References 13 publications

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“…In another work, Zagreb connection indices were explored in the context of CNN, as discussed in [28]. In [17], dominant topological indices for cellular neural networks were scrutinized and compared. In the work by Arshad et al, presented in [3] intriguing topological properties including optimal routing were unveiled for this specific class of neural networks.…”

Section: Figure 1 Cnn and Its Architecturementioning

confidence: 99%

Spectral Analysis of Cellular Neural Network: Unveiling Network Parameters and Graph Characteristics

Saravanan,

Ganesan

2024

Preprint

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Cellular Neural Network (CNN) finds application in a wide array of parallel processing tasks, such as image processing, non-linear operations, generating geometric maps, and high-speed computations. Functioning as an analogue paradigm, CNN comprises an array of cells interconnected at a local level. These cells can be arranged in an array of $m \times n$ identical cells in a rectangular grid. Graphical representation is achieved by representing cells as vertices and their connections as edges, denoted as $\Gamma_{m,n}$. This paper aims to compute spectrum based results for the CNN. To accomplish this, we determine the Laplacian and the signless Laplacian eigenvalues of $\Gamma_{m,n}$. Utilising these results, we derive a comprehensive set of network-related parameters, including the Kirchhoff index, average path length, mean first passage time, the number of spanning trees, the Estrada index, and the resolvent Estrada index. Furthermore, we delve into graph-related parameters encompassing graph energy and spectral radius to gain deeper insights into the characteristics of $\Gamma_{m,n}$. To streamline our analysis, we design an algorithm to calculate the network-related parameters, as mentioned earlier. Moreover, results are enhanced by the inclusion of numerical tables and vibrant 3D plots that visually depict Laplacian and signless Laplacian energies for specific configurations. Finally, we underscore the application of energy for image segmentation by selecting suitable CNN sizes based on energy, which provides precise results that reduce evaluation time and significantly enhance diagnostic accuracy in image processing. 2020 Mathematics Subject Classification. 05C50, 05C76, 05C90, 68R10, 94C15.

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Section: Figure 1 Cnn and Its Architecturementioning

confidence: 99%

Spectral Analysis of Cellular Neural Network: Unveiling Network Parameters and Graph Characteristics

Saravanan,

Ganesan

2024

Preprint

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“…Topology optimization and Zagreb connection indices for cellular neural network are studied in [30,33]. Recently in 2021, the comparison and analysis between the dominating topological indices are determined for the cellular neural network [34]. Some topological indices have been calculated for cellular neural network, and are prominence their importance, but still many topological indices have not been calculated.…”

Section: Applications and Importancementioning

confidence: 99%

A Study of Cellular Neural Networks with Vertex-Edge Topological Descriptors

Husain¹,

Imran²,

Ahmad³

et al. 2022

Computers, Materials &Amp; Continua

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The Cellular Neural Network (CNN) has various parallel processing applications, image processing, non-linear processing, geometric maps, highspeed computations. It is an analog paradigm, consists of an array of cells that are interconnected locally. Cells can be arranged in different configurations. Each cell has an input, a state, and an output. The cellular neural network allows cells to communicate with the neighbor cells only. It can be represented graphically; cells will represent by vertices and their interconnections will represent by edges. In chemical graph theory, topological descriptors are used to study graph structure and their biological activities. It is a single value that characterizes the whole graph. In this article, the vertex-edge topological descriptors have been calculated for cellular neural network. Results can be used for cellular neural network of any size. This will enhance the applications of cellular neural network in image processing, solving partial differential equations, analyzing 3D surfaces, sensory-motor organs, and modeling biological vision.

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“…A combined discrete branch of graph theory and mathematical structures especially deals in studying and modeling structures properties of networks with respect to mathematical graph invariants quantities is called structural graph theory. By showing vertices and edges of graphical structure for a network, it can be visualized in a unique way for observing the properties of that network [5]. For the study of physical and structural properties of a specific network, a simple transformation is used which converts structure into a graph, for the help of mathematicians.…”

Section: Introductionmentioning

confidence: 99%

Connection Number of Generalized two dimensional Rhombohedral Plane composed by p-sided Polygon

Mubashar

İnç

Hussain

et al. 2022

Preprint

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Gutman and Trinajstic deducted that total π-energy of a chemical molecule depends upon a numeric value which is termed as zagreb index. In that same report, they also defined a term for a particular atom with respect to other atom which is away from at a distance two. This quantity provides π-energy for a molecule. Now a days, in subject context, this quantity is termed as connection number. In this paper, we have discovered a new graph. It is composed of p-sided polygon in two dimensional rhombohedral plane. This 2D network astonishingly a new discovery in literature, its topological properties are explained via different connection numbers.

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Dominating Topological Analysis and Comparison of the Cellular Neural Network

Cited by 6 publications

References 13 publications

Spectral Analysis of Cellular Neural Network: Unveiling Network Parameters and Graph Characteristics

Spectral Analysis of Cellular Neural Network: Unveiling Network Parameters and Graph Characteristics

A Study of Cellular Neural Networks with Vertex-Edge Topological Descriptors

Connection Number of Generalized two dimensional Rhombohedral Plane composed by p-sided Polygon

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