FAULT-TOLERANT METRIC DIMENSION OF CIRCULANT GRAPHS [PDF]
Facta Universitatis, Series: Mathematics and Informatics, 2019 A set $W$ of vertices in a graph $G$ is called a resolving setfor $G$ if for every pair of distinct vertices $u$ and $v$ of $G$ there exists a vertex $w \in W$ such that the distance between $u$ and $w$ is different from the distance between $v$ and $w$. The cardinality of a minimum resolving set is called the metric dimension of $G$, denoted by $\beta(
Seyedi, Narjes, Maimani, Hamid Reza
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On Resolvability- and Domination-Related Parameters of Complete Multipartite Graphs
Mathematics, 2022 Graphs of order n with fault-tolerant metric dimension n have recently been characterized.This paper points out an error in the proof of this characterization. We show that the complete multipartite graphs also have the fault-tolerant metric dimension n,
Sakander Hayat, Asad Khan, Yubin Zhong
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The disjointness of stabilizer codes and limitations on fault-tolerant logical gates [PDF]
, 2017 Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for these codes, the
Jochym-O'Connor, Tomas +2 more
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The Application of Fault-Tolerant Partition Resolvability in Cycle-Related Graphs
Applied Sciences, 2022 The concept of metric-related parameters permeates all of graph theory and plays an important role in diverse networks, such as social networks, computer networks, biological networks and neural networks.
Kamran Azhar +4 more
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The fault-tolerant metric dimension of the king’s graph [PDF]
Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2017 openaire +3 more sources
Bounds for metric dimension and defensive $k$-alliance of graphs under deleted lexicographic product [PDF]
Transactions on Combinatorics, 2020 Metric dimension and defensive $k$-alliance number are two distance-based graph invariants which have applications in robot navigation, quantitative analysis of secondary RNA structures, national defense and fault-tolerant computing.
Kinkar Chandra Das, Mostafa Tavakoli
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The Fault-Tolerant Metric Dimension of Cographs [PDF]
, 2019 arXiv admin note: text overlap with arXiv:1806 ...
Duygu Vietz, Egon Wanke
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Sequential Circuit Design for Embedded Cryptographic Applications Resilient to Adversarial Faults [PDF]
, 2007 In the relatively young field of fault-tolerant cryptography, the main research effort has focused exclusively on the protection of the data path of cryptographic circuits.
Gaubatz, Gunnar +3 more
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Fault-Tolerant Resolvability in Some Classes of Subdivision Graphs
Journal of Mathematics, 2022 The concept of resolving sets (RSs) and metric dimension (MD) invariants have a wide range of applications in robot navigation, computer networks, and chemical structure. RS has been used as a sensor in an indoor positioning system to find an interrupter.
Muhammad Faheem +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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