Computation of the Double Metric Dimension in Convex Polytopes

Pan, Langxing; Ahmad, Muhammad; Zahid, Zohaib; Zafar, Sohail

doi:10.1155/2021/9958969

Cited by 7 publications

(5 citation statements)

References 25 publications

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“…Further, MDRSs of prisms and Hamming networks were computed in [30] and [31]. Another study by Pan et al [32], showed the DMD was always the same in the case of some convex polytopes. Also, the MDRSs for the chordal ring networks is discussed in [33].…”

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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“…Ahmad et al discussed the problem of finding the minimal resolving set and MDRS for line graphs of kayak paddles graphs [30]. The authors in [31,32] presented some families of convex polytopes with constant DMD. While solving the MDRS problem, certain families of Harary graphs, layer-sun graphs have also been investigated in [33,34], respectively.…”

Section: Introductionmentioning

confidence: 99%

Minimal Doubly Resolving Sets of Certain Families of Toeplitz Graph

Ahmad¹,

Jarad²,

Zahid³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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The doubly resolving sets are a natural tool to identify where diffusion occurs in a complicated network. Many realworld phenomena, such as rumour spreading on social networks, the spread of infectious diseases, and the spread of the virus on the internet, may be modelled using information diffusion in networks. It is obviously impractical to monitor every node due to cost and overhead limits because there are too many nodes in the network, some of which may be unable or unwilling to send information about their state. As a result, the source localization problem is to find the number of nodes in the network that best explains the observed diffusion. This problem can be successfully solved by using its relationship with the well-studied related minimal doubly resolving set problem, which minimizes the number of observers required for accurate detection. This paper aims to investigate the minimal doubly resolving set for certain families of Toeplitz graph T n (1, t), for t ≥ 2 and n ≥ t + 2. We come to the conclusion that for T n (1, 2), the metric and double metric dimensions are equal and for T n (1, 4), the double metric dimension is exactly one more than the metric dimension. Also, the double metric dimension for T n (1, 3) is equal to the metric dimension for n = 5, 6, 7 and one greater than the metric dimension for n ≥ 8.

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“…To find the smallest possible DRS, a variety of graph families have been examined, such as those involving prisms [31], convex polytopes [32], and Hamming graphs [33]. e MDRSs of different convex polytope structures were examined by Pan et al [34] and Ahmad et al [35]. Minimal order resolving sets and MDRSs of cocktail and jellyfish graphs were calculated by Liu and others [36].…”

Section: Introductionmentioning

confidence: 99%

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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Computation of the Double Metric Dimension in Convex Polytopes

Cited by 7 publications

References 25 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

Minimal Doubly Resolving Sets of Certain Families of Toeplitz Graph

Double Metric Resolvability in Convex Polytopes

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