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The Application of Fault-Tolerant Partition Resolvability in Cycle-Related Graphs.

Authors :
Azhar, Kamran
Zafar, Sohail
Kashif, Agha
Aljaedi, Amer
Albalawi, Umar
Source :
Applied Sciences (2076-3417); Oct2022, Vol. 12 Issue 19, p9558, 13p
Publication Year :
2022

Abstract

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. The graph parameters include an incredible tool for analyzing the abstract structures of networks. An important metric-related parameter is the partition dimension of a graph holding auspicious applications in telecommunication, robot navigation and geographical routing protocols. A fault-tolerant resolving partition is a preference for the concept of a partition dimension. A system is fault-tolerant if failure of any single unit in the originally used chain is replaced by another chain of units not containing the faulty unit. Due to the optimal fault tolerance, cycle-related graphs have applications in network analysis, periodic scheduling and surface reconstruction. In this paper, it is shown that the partition dimension (PD) and fault-tolerant partition dimension (FTPD) of cycle-related graphs, including kayak paddle and flower graphs, are constant and free from the order of these graphs. More explicitly, the FTPD of kayak paddle and flower graphs is four, whereas the PD of flower graphs is three. Finally, an application of these parameters in a scenario of installing water reservoirs in a locality has also been furnished in order to verify our findings. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
20763417
Volume :
12
Issue :
19
Database :
Complementary Index
Journal :
Applied Sciences (2076-3417)
Publication Type :
Academic Journal
Accession number :
159675567
Full Text :
https://doi.org/10.3390/app12199558