scholarly journals Lower and Upper Bounds of Fractional Metric Dimension of Connected Networks

2021 ◽  
Vol 5 (4) ◽  
pp. 276
Author(s):  
Muhammad Javaid ◽  
Muhammad Kamran Aslam ◽  
Muhammad Imran Asjad ◽  
Bander N. Almutairi ◽  
Mustafa Inc ◽  
...  
Keyword(s):  
Large Scale ◽  
Chemical Compounds ◽  
Vital Role ◽  
Molecular Networks ◽  
Metric Dimension ◽  
Weighted Version ◽  
Shortest Distance ◽  
Metric Dimensions ◽  
Large Scale Networks ◽  
2D And 3D

The distance centric parameter in the theory of networks called by metric dimension plays a vital role in encountering the distance-related problems for the monitoring of the large-scale networks in the various fields of chemistry and computer science such as navigation, image processing, pattern recognition, integer programming, optimal transportation models and drugs discovery. In particular, it is used to find the locations of robots with respect to shortest distance among the destinations, minimum consumption of time, lesser number of the utilized nodes, and to characterize the chemical compounds, having unique presentations in molecular networks. After the arrival of its weighted version, known as fractional metric dimension, the rectification of distance-related problems in the aforementioned fields has revived to a great extent. In this article, we compute fractional as well as local fractional metric dimensions of web-related networks called by subdivided QCL, 2-faced web, 3-faced web, and antiprism web networks. Moreover, we analyse their final results using 2D and 3D plots.

scholarly journals Boundedness of Convex Polytopes Networks via Local Fractional Metric Dimension

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Muhammad Javaid ◽  
Hassan Zafar ◽  
Amer Aljaedi ◽  
Abdulaziz Mohammad Alanazi
Keyword(s):  
Convex Polytopes ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Molecular Networks ◽  
Metric Dimension ◽  
Optimal Solutions ◽  
Weighted Version ◽  
Shortest Distance ◽  
Metric Dimensions ◽  
And Chemical Properties

Metric dimension is one of the distance-based parameter which is frequently used to study the structural and chemical properties of the different networks in the various fields of computer science and chemistry such as image processing, pattern recognition, navigation, integer programming, optimal transportation models, and drugs discovery. In particular, it is used to find the locations of robots with respect to shortest distance among the destinations, minimum consumption of time, and lesser number of the utilized nodes and to characterize the chemical compounds having unique presentation in molecular networks. The fractional metric dimension being a latest developed weighted version of the metric dimension is used in the distance-related problems of the aforementioned fields to find their nonintegral optimal solutions. In this paper, we have formulated the local resolving neighborhoods with their cardinalities for all the edges of the convex polytopes networks to compute their local fractional metric dimensions in the form of exact values and sharp bounds. Moreover, the boundedness of all the obtained results is also proved.

scholarly journals Classification of Upper Bound Sequences of Local Fractional Metric Dimension of Rotationally Symmetric Hexagonal Planar Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-24
Author(s):  
Shahbaz Ali ◽  
Muhammad Khalid Mahmood ◽  
Fairouz Tchier ◽  
F. M. O. Tawfiq
Keyword(s):  
Image Processing ◽  
Chemical Engineering ◽  
Chemical Compounds ◽  
Vital Role ◽  
Metric Dimension ◽  
Integer Programming Problem ◽  
Rotationally Symmetric ◽  
Metric Dimensions ◽  
Planar Networks

The term metric or distance of a graph plays a vital role in the study to check the structural properties of the networks such as complexity, modularity, centrality, accessibility, connectivity, robustness, clustering, and vulnerability. In particular, various metrics or distance-based dimensions of different kinds of networks are used to resolve the problems in different strata such as in security to find a suitable place for fixing sensors for security purposes. In the field of computer science, metric dimensions are most useful in aspects such as image processing, navigation, pattern recognition, and integer programming problem. Also, metric dimensions play a vital role in the field of chemical engineering, for example, the problem of drug discovery and the formation of different chemical compounds are resolved by means of some suitable metric dimension algorithm. In this paper, we take rotationally symmetric and hexagonal planar networks with all possible faces. We find the sequences of the local fractional metric dimensions of proposed rotationally symmetric and planar networks. Also, we discuss the boundedness of sequences of local fractional metric dimensions. Moreover, we summarize the sequences of local fractional metric dimension by means of their graphs.

scholarly journals Bounds of Fractional Metric Dimension and Applications with Grid-Related Networks

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1383
Author(s):  
Ali H. Alkhaldi ◽  
Muhammad Kamran Aslam ◽  
Muhammad Javaid ◽  
Abdulaziz Mohammed Alanazi
Keyword(s):  
Metric Dimension ◽  
Hard Problem ◽  
Np Hard ◽  
Weighted Version ◽  
Sharp Bounds ◽  
Np Hard Problem ◽  
Metric Dimensions

Metric dimension of networks is a distance based parameter that is used to rectify the distance related problems in robotics, navigation and chemical strata. The fractional metric dimension is the latest developed weighted version of metric dimension and a generalization of the concept of local fractional metric dimension. Computing the fractional metric dimension for all the connected networks is an NP-hard problem. In this note, we find the sharp bounds of the fractional metric dimensions of all the connected networks under certain conditions. Moreover, we have calculated the fractional metric dimension of grid-like networks, called triangular and polaroid grids, with the aid of the aforementioned criteria. Moreover, we analyse the bounded and unboundedness of the fractional metric dimensions of the aforesaid networks with the help of 2D as well as 3D plots.

scholarly journals Computing LF-Metric Dimension of Generalized Gear Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Hassan Zafar ◽  
Muhammad Javaid ◽  
Ebenezer Bonyah
Keyword(s):  
Structural Properties ◽  
Metric Dimension ◽  
Sharp Bounds ◽  
Shortest Distance ◽  
Metric Dimensions

The parameter of distance in the theory of networks plays a key role to study the different structural properties of the understudy networks or graphs such as symmetry, assortative, connectivity, and clustering. For the purpose, with the help of the parameter of distance, various types of metric dimensions have been defined to find the locations of machines (or robots) with respect to the minimum consumption of time, the shortest distance among the destinations, and the lesser number of utilized nodes as places of the objects. In this article, the latest derived form of metric dimension called as LF-metric dimension is studied, and various results for the generalized gear networks are obtained in the form of exact values and sharp bounds under certain conditions. The LF-metric dimension of some particular cases of generalized gear networks (called as generalized wheel networks) is also illustrated. Moreover, the bounded and unboundedness of the LF-metric dimension for all obtained results is also presented.

scholarly journals On the Upper Bounds of Fractional Metric Dimension of Symmetric Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Muhammad Javaid ◽  
Muhammad Kamran Aslam ◽  
Jia-Bao Liu
Keyword(s):  
Image Processing ◽  
Drug Discovery ◽  
Computer Science ◽  
Chemical Compounds ◽  
Upper Bounds ◽  
Metric Dimension ◽  
Rotationally Symmetric ◽  
Metric Dimensions ◽  
Structural Aspects ◽  
Symmetric Networks

Distance-based numeric parameters play a pivotal role in studying the structural aspects of networks which include connectivity, accessibility, centrality, clustering modularity, complexity, vulnerability, and robustness. Several tools like these also help to resolve the issues faced by the different branches of computer science and chemistry, namely, navigation, image processing, biometry, drug discovery, and similarities in chemical compounds. For this purpose, in this article, we are considering a family of networks that exhibits rotationally symmetric behaviour known as circular ladders consisting of triangular, quadrangular, and pentagonal faced ladders. We evaluate their upper bounds of fractional metric dimensions of the aforementioned networks.

scholarly journals Contribution of Ionotropic Glutamatergic Receptors to Excitability and Attentional Signals in Macaque Frontal Eye Field

2021 ◽  
Author(s):  
Miguel Dasilva ◽  
Christian Brandt ◽  
Marc Alwin Gieselmann ◽  
Claudia Distler ◽  
Alexander Thiele
Keyword(s):  
Attentional Control ◽  
Large Scale ◽  
Neuronal Excitability ◽  
Cell Types ◽  
Receptor Activation ◽  
Frontal Eye Field ◽  
Control Signals ◽  
Cognitive Operations ◽  
Eye Field ◽  
Large Scale Networks

Abstract Top-down attention, controlled by frontal cortical areas, is a key component of cognitive operations. How different neurotransmitters and neuromodulators flexibly change the cellular and network interactions with attention demands remains poorly understood. While acetylcholine and dopamine are critically involved, glutamatergic receptors have been proposed to play important roles. To understand their contribution to attentional signals, we investigated how ionotropic glutamatergic receptors in the frontal eye field (FEF) of male macaques contribute to neuronal excitability and attentional control signals in different cell types. Broad-spiking and narrow-spiking cells both required N-methyl-D-aspartic acid and α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor activation for normal excitability, thereby affecting ongoing or stimulus-driven activity. However, attentional control signals were not dependent on either glutamatergic receptor type in broad- or narrow-spiking cells. A further subdivision of cell types into different functional types using cluster-analysis based on spike waveforms and spiking characteristics did not change the conclusions. This can be explained by a model where local blockade of specific ionotropic receptors is compensated by cell embedding in large-scale networks. It sets the glutamatergic system apart from the cholinergic system in FEF and demonstrates that a reduction in excitability is not sufficient to induce a reduction in attentional control signals.

scholarly journals How does the position of firms in the supply chain affect their performance? An empirical study

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Siddharth Arora ◽  
Alexandra Brintrup
Keyword(s):  
Supply Chain ◽  
Empirical Data ◽  
Large Scale ◽  
Individual Performance ◽  
Supply Network ◽  
Supply Chain Networks ◽  
Focal Firm ◽  
Cooperative Competition ◽  
Large Scale Networks ◽  
The Relationship

AbstractThe relationship between a firm and its supply chain has been well studied, however, the association between the position of firms in complex supply chain networks and their performance has not been adequately investigated. This is primarily due to insufficient availability of empirical data on large-scale networks. To addresses this gap in the literature, we investigate the relationship between embeddedness patterns of individual firms in a supply network and their performance using empirical data from the automotive industry. In this study, we devise three measures that characterize the embeddedness of individual firms in a supply network. These are namely: centrality, tier position, and triads. Our findings caution us that centrality impacts individual performance through a diminishing returns relationship. The second measure, tier position, allows us to investigate the concept of tiers in supply networks because we find that as networks emerge, the boundaries between tiers become unclear. Performance of suppliers degrade as they move away from the focal firm (i.e., Toyota). The final measure, triads, investigates the effect of buying and selling to firms that supply the same customer, portraying the level of competition and cooperation in a supplier’s network. We find that increased coopetition (i.e., cooperative competition) is a performance enhancer, however, excessive complexity resulting from being involved in both upstream and downstream coopetition results in diminishing performance. These original insights help understand the drivers of firm performance from a network perspective and provide a basis for further research.

Sign in / Sign up

Export Citation Format

Share Document