Minimal Doubly Resolving Sets of Some Classes of Convex Polytopes

Ahmad, Muhammad; Alrowaili, Dalal; Zahid, Zohaib; Siddique, Imran; Iampan, Aiyared

doi:10.1155/2022/1818734

Cited by 5 publications

(1 citation statement)

References 32 publications

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“…The problems of MD and MDRS for cocktail party networks and jellyfish networks have been investigated in [34]. Moreover, the generalized results for the DMD problem of certain convex polytope structures were derived by Ahmad et al [35], [36].…”

Section: Introductionmentioning

confidence: 99%

A Study on Minimal Doubly Resolving Sets of Certain Families of Networks

et al. 2023

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The suppression of harmful information and even its diffusion can be predicted and delayed by precisely finding sources with limited resources. The doubly resolving sets (DRSs) play a crucial role in determining where diffusion occurs in a network. Source detection problems are among the most challenging and exciting problems in complex networks. This problem has great significance in controlling any diffusion outbreak. The detection of a virus source in a network is basically locating a node that spreads the observed diffusion. This problem can be solved by using its connection to the well-known and well-studied minimal doubly resolving set (MDRS) problem, which reduces the number of observers needed to get an accurate answer. In this article, we investigate the MDRSs for the families of kayak paddle networks KP (r,s,t) and lollipop networks L (r,s) . It is concluded that the cardinality of MDRSs for KP (r,s,t) is bounded, and it is unbounded for L (r,s) .

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Section: Introductionmentioning

confidence: 99%

A Study on Minimal Doubly Resolving Sets of Certain Families of Networks

et al. 2023

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Double Metric Resolvability in Convex Polytopes

Ahmad

Alrowaili

Ali

et al. 2022

Journal of Mathematics

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Nowadays, the study of source localization in complex networks is a critical issue. Localization of the source has been investigated using a variety of feasible models. To identify the source of a network’s diffusion, it is necessary to find a vertex from which the observed diffusion spreads. Detecting the source of a virus in a network is equivalent to finding the minimal doubly resolving set (MDRS) in a network. This paper calculates the doubly resolving sets (DRSs) for certain convex polytope structures to calculate their double metric dimension (DMD). It is concluded that the cardinality of MDRSs for these convex polytopes is finite and constant.

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Studies of Chordal Ring Networks via Double Metric Dimensions

Ahmad

Zahid

Javaid

et al. 2022

Mathematical Problems in Engineering

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Locating the sources of information spreading in networks including tracking down the origins of epidemics, rumors in social networks, and online computer viruses, has a wide range of applications. In many situations, identifying where an epidemic started, or which node in a network served as the source, is crucial. But it can be difficult to determine the root of an outbreak, especially when data are scarce and noisy. The goal is to find the source of the infection by analysing data provided by only a limited number of observers, such as nodes that can indicate when and where they are infected. Our goal is to investigate where the least number of observers should be placed, which is similar to how to figure out the minimal doubly resolving sets in the network. In this paper, we calculate the double metric dimension of chordal ring networks C R n 1,3,5 by describing their minimal doubly resolving sets.

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Minimal Doubly Resolving Sets of Some Classes of Convex Polytopes

Cited by 5 publications

References 32 publications

A Study on Minimal Doubly Resolving Sets of Certain Families of Networks

A Study on Minimal Doubly Resolving Sets of Certain Families of Networks

Double Metric Resolvability in Convex Polytopes

Studies of Chordal Ring Networks via Double Metric Dimensions

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