Forcing Parameters in Fully Connected Cubic Networks

Rao, Yongsheng; Kosari, Saeed; Anitha, J.; Rajasingh, Indra; Rashmanlou, Hossein

doi:10.3390/math10081263

Cited by 6 publications

(4 citation statements)

References 15 publications

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“…From Figure 1, it can be seen that the relative residual norm of CGS2,SCGS, GCGS CGS, and GCGS2 methods shows irregular convergence behavior, while the relative residual norm of the QMRGCGS2 method tends to show regular convergence behavior. Tat is to say, the QMRGCGS2 method has smoother convergence behavior than the CGS method and GCGS2 method [41][42][43]. Finally, CGS2 and CGS methods with good performance are selected to compare their performance with the proposed QMRGCGS2 method for practical application problems.…”

Section: Applicationmentioning

confidence: 99%

Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations

2022

Journal of Mathematics

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The complexity of open linear algebraic equations makes it difficult to obtain analytical solutions, and preprocessing techniques can be applied to coefficient matrices, which has become an effective method to accelerate the convergence of iterative methods. Therefore, it is important to preprocess the structure of open linear algebraic equations to reduce their complexity. Open linear algebraic equations can be divided into symmetric linear equations and asymmetric linear equations. The former is based on 2 × 2. The latter is preprocessed by the improved QMRGCGS method, and the applications of the two methods are analyzed, respectively. The experimental results show that when the step is 500, the pretreatment time of quasi-minimal residual generalized conjugate gradient square 2 method is 34.23 s, that of conjugate gradient square 2 method is 35.14 s, and that of conjugate gradient square method is 45.20 s, providing a new reference method and idea for solving and preprocessing non-closed linear algebraic equations.

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Section: Applicationmentioning

confidence: 99%

Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations

2022

Journal of Mathematics

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“…FG theory is a significant and extensive area of research with a primary focus on connectivity. Different fuzzy connectivity measures were discussed in [5][6][7][8][9][10][11][12][13][14], 15-19. Mathew and Sunitha [20,21] examined the concepts of edge connectivity, vertex connectivity, and cycle connectivity in FGs.…”

Section: Introductionmentioning

confidence: 99%

Generalized connectivity in cubic fuzzy graphs with application in the trade deficit problem

Rao,

Chen,

Ahmad

et al. 2024

Front. Phys.

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Cubic fuzzy graphs (CFGs) offer greater utility as compared to interval-valued fuzzy graphs and fuzzy graphs due to their ability to represent the degree of membership for vertices and edges using both interval and fuzzy number forms. The significance of these concepts motivates us to analyze and interpret intricate networks, enabling more effective decision making and optimization in various domains, including transportation, social networks, trade networks, and communication systems. This paper introduces the concepts of vertex and edge connectivity in CFGs, along with discussions on partial cubic fuzzy cut nodes and partial cubic fuzzy edge cuts, and presents several related results with the help of some examples to enhance understanding. In addition, this paper introduces the idea of partial cubic α-strong and partial cubic δ-weak edges. An example is discussed to explain the motivation behind partial cubic α-strong edges. Moreover, it delves into the introduction of generalized vertex and edge connectivity in CFGs, along with generalized partial cubic fuzzy cut nodes and generalized partial cubic fuzzy edge cuts. Relevant results pertaining to these concepts are also discussed. As an application, the concept of generalized partial cubic fuzzy edge cuts is applied to identify regions that are most affected by trade deficits resulting from street crimes. Finally, the research findings are compared with the existing method to demonstrate their suitability and creativity.

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“…Study on VG and results from these graphs were introduced by Kosari et al [7][8][9][10]. Furthermore, a review was carried out on different types of FGs, and the new results were studied [11][12][13]. In graph theory, a dominating set (DS) for a graph G is a subset D of its vertices, such that any vertex of G is either in D or has a neighbor in D. The domination number γ(G) is the number of vertices in a smallest DS for G. DSs are of practical interest in several areas.…”

Section: Introductionmentioning

confidence: 99%

A Novel Domination in Vague Influence Graphs with an Application

Shi,

Cai,

Talebi

et al. 2024

Axioms

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Vague influence graphs (VIGs) are well articulated, useful and practical tools for managing the uncertainty preoccupied in all real-life difficulties where ambiguous facts, figures and explorations are explained. A VIG gives the information about the effect of a vertex on the edge. In this paper, we present the domination concept for VIG. Some issues and results of the domination in vague graphs (VGs) are also developed in VIGs. We defined some basic notions in the VIGs such as the walk, path, strength of In-pair , strong In-pair, In-cut vertex, In-cut pair (CP), complete VIG and strong pair domination number in VIG. Finally, an application of domination in illegal drug trade was introduced.

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Forcing Parameters in Fully Connected Cubic Networks

Cited by 6 publications

References 15 publications

Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations

Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations

Generalized connectivity in cubic fuzzy graphs with application in the trade deficit problem

A Novel Domination in Vague Influence Graphs with an Application

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