Results 21 to 30 of about 684 (218)
On Fault-Tolerant Resolving Sets of Some Families of Ladder Networks
Complexity, 2021 In computer networks, vertices represent hosts or servers, and edges represent as the connecting medium between them. In localization, some special vertices (resolving sets) are selected to locate the position of all vertices in a computer network. If an
Hua Wang +4 more
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The fault-tolerant metric dimension of the king’s graph [PDF]
Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya, 2017 exaly +2 more sources
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 Fault-Tolerant Metric Dimension of Cographs [PDF]
, 2019 arXiv admin note: text overlap with arXiv:1806 ...
Duygu Vietz, Egon Wanke
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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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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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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 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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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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