Metric and fault-tolerant metric dimension for GeSbTe superlattice chemical structure. [PDF]
PLoS ONE, 2023 The concept of metric dimension has many applications, including optimizing sensor placement in networks and identifying influential persons in social networks, which aids in effective resource allocation and focused interventions; finding the source of ...
Liu Liqin +4 more
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Optimal Fault-Tolerant Resolving Set of Power Paths
Mathematics, 2023 In a simple connected undirected graph G, an ordered set R of vertices is called a resolving set if for every pair of distinct vertices u and v, there is a vertex w∈R such that d(u,w)≠d(v,w).
Laxman Saha +4 more
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Fault-Tolerant Metric Dimension of Circulant Graphs [PDF]
Mathematics, 2022 Let G be a connected graph with vertex set V(G) and d(u,v) be the distance between the vertices u and v. A set of vertices S={s1,s2,…,sk}⊂V(G) is called a resolving set for G if, for any two distinct vertices u,v∈V(G), there is a vertex si∈S such that d ...
Laxman Saha +4 more
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Edge-Version of Fault-Tolerant Resolvability in Networks
IEEE AccessFault tolerance refers to a system’s capacity to continue functioning as intended, even when one of its components fails. Such a system is known as a fault-tolerant, self-stable system.
Muhammad Faheem +4 more
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Fault-tolerance in metric dimension of boron nanotubes lattices [PDF]
Frontiers in Computational Neuroscience, 2023 The concept of resolving set and metric basis has been very successful because of multi-purpose applications both in computer and mathematical sciences.
Zafar Hussain, Muhammad Mobeen Munir
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Fault tolerance in para-line network topologies: theory and applications in smart systems [PDF]
Scientific ReportsThis study explores the fault-tolerant metric dimension (FTMD) of the para-line network, which is derived from the n-sunlet network, a significant category of networks created by subdividing and transforming cycle-based networks to simulate greater ...
Sanaa Ahmed Bajri +5 more
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Optimizing emergency response services in urban areas through the fault-tolerant metric dimension of hexagonal nanosheet [PDF]
Scientific ReportsIn this work, we find the fault-tolerant metric dimension of a hexagonal nanosheet. This concept ensures robust identity of vertices inside a graph, even in situations in which a few resolving vertices fail.
Yaoyao Tu +5 more
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Fault-Tolerant Resolvability and Extremal Structures of Graphs
Mathematics, 2019 In this paper, we consider fault-tolerant resolving sets in graphs. We characterize n-vertex graphs with fault-tolerant metric dimension n, n − 1 , and 2, which are the lower and upper extremal cases.
Hassan Raza +3 more
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Fault-Tolerant Metric Dimension and Applications: Zero-Divisor Graph of Upper Triangular Matrices
MathematicsGraph invariants play a crucial role in understanding the structural and combinatorial characteristics of graphs. The fault-tolerant metric dimension, as a significant graph invariant, finds applications in diverse areas such as robust network ...
Latif Abdelmalek Hanna +2 more
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Robust mesh generation for electromagnetic models with geometric defects through node alignment and mesh boolean operations [PDF]
Scientific ReportsThis paper presents a mesh fault-tolerant repair algorithm tailored to address common geometric issues inherent in electromagnetic models. During the actual production design phase, electromagnetic models frequently display a variety of geometric ...
Z. H. Gao +5 more
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