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A Study on Minimal Doubly Resolving Sets of Certain Families of Networks
IEEE Access, 2023 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 ...
Muhammad Ahmad +3 more
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Minimal Doubly Resolving Sets of Some Classes of Convex Polytopes
Journal of Mathematics, 2022 Source localization is one of the most challenging problems in complex networks. Monitoring and controlling complex networks is of great interest for understanding different types of systems, such as biological, technological, and complex physical ...
Muhammad Ahmad +4 more
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Computing Minimal Doubly Resolving Sets and the Strong Metric Dimension of the Layer Sun Graph and the Line Graph of the Layer Sun Graph [PDF]
Complexity, 2020 Let G be a finite, connected graph of order of, at least, 2 with vertex set VG and edge set EG. A set S of vertices of the graph G is a doubly resolving set for G if every two distinct vertices of G are doubly resolved by some two vertices of S.
Jia-Bao Liu, Ali Zafari
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Metric Dimension, Minimal Doubly Resolving Sets, and the Strong Metric Dimension for Jellyfish Graph and Cocktail Party Graph [PDF]
Complexity, 2020 Let Γ be a simple connected undirected graph with vertex set VΓ and edge set EΓ. The metric dimension of a graph Γ is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely ...
Jia-Bao Liu, Ali Zafari, Hassan Zarei
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A bridge between the minimal doubly resolving set problem in (folded) hypercubes and the coin weighing problem [PDF]
Discrete Applied Mathematics, 2022 In this paper, we consider the minimal doubly resolving set problem in Hamming graphs, hypercubes and folded hypercubes. We prove that the minimal doubly resolving set problem in hypercubes is equivalent to the coin weighing problem. Then we answer an open question on the minimal doubly resolving set problem in hypercubes.
Changhong Lu, Qingjie Ye
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Minimal doubly resolving sets and the strong metric dimension of Hamming graphs
Applicable Analysis and Discrete Mathematics, 2012 We consider the problem of determining the cardinality ?(H2,k) of minimal doubly resolving sets of Hamming graphs H2,k. We prove that for k ? 6 every minimal resolving set of H2,k is also a doubly resolving set, and, consequently, ?(H2,k) is equal to the metric dimension of H2,k, which is known from the literature.
Jozef Kratica +3 more
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Minimal doubly resolving sets of antiprism and Möbius ladders
Miskolc Mathematical Notes, 2022 Summary: Consider a simple connected graph \(G=(V(G),E(G))\), where \(V(G)\) represents the vertex set and \(E(G)\) represents the edge set respectively. A subset \(W\) of \(V(G)\) is called a resolving set for a graph \(G\) if for every two distinct vertices \(x,y\in V(G)\), there exist some vertex \(w\in W\) such that \(d(x,w)\neq d(y,w)\), where \(d(
Sultan, Saba +3 more
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Computation of the Double Metric Dimension in Convex Polytopes
Journal of Mathematics, 2021 A source detection problem in complex networks has been studied widely. Source localization has much importance in order to model many real-world phenomena, for instance, spreading of a virus in a computer network, epidemics in human beings, and rumor ...
Liying Pan +3 more
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Double Metric Resolvability in Convex Polytopes
Journal of Mathematics, 2022 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.
Muhammad Ahmad +4 more
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On Minimal Doubly Resolving Sets of Circulant Graphs [PDF]
Acta Mechanica Slovaca, 2017 Consider a simple connected undirected graph G = (VG ,EG), where VG represents the vertex set and EG represents the edge set respectively. A subset B of VG is called a resolving set if for every two distinct vertices x, y of G there is a vertex v in set B such that d(x,v) ≠ d(y,v).
Ali Ahmad, Saba Sultan
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