On Fault-Tolerant Resolving Sets of Some Families of Ladder Networks

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 arbitrary vertex stopped working and selected...

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Bibliographic Details
Published in:Complexity (New York, N.Y.) N.Y.), 2021, Vol.2021 (1)
Main Authors: Wang, Hua, Azeem, Muhammad, Nadeem, Muhammad Faisal, Ur-Rehman, Ata, Aslam, Adnan
Format: Article
Language:English
Subjects:
Apexes
Computer networks
Fault tolerance
Graph theory
Inequality
Sensors
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Summary: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 arbitrary vertex stopped working and selected vertices still remain the resolving set, then the chosen set is called as the fault-tolerant resolving set. The least number of vertices in such resolving sets is called the fault-tolerant metric dimension of the network. Because of the variety of applications of the metric dimension in different areas of sciences, many generalizations were proposed, and fault tolerant is one of them. In this paper, we computed the fault-tolerant metric dimension of triangular snake, ladder, Mobius ladder, and hexagonal ladder networks. It is important to observe that, in all these classes of networks, the fault-tolerant metric dimension and metric dimension differ by 1.
ISSN:1076-2787
1099-0526
DOI:10.1155/2021/9939559