Optimal Multi-Level Fault-Tolerant Resolving Sets of Circulant Graph C(n : 1, 2)

Laxman Saha, Bapan Das, Kalishankar Tiwary, Kinkar Chandra Das*, Yilun Shang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
13 Downloads (Pure)

Abstract

Let G=(V(G),E(G))
be a simple connected unweighted graph. A set R⊂V(G)
is called a fault-tolerant resolving set with the tolerance level k if the cardinality of the set Sx,y={w∈R:d(w,x)≠d(w,y)}
is at least k for every pair of distinct vertices x,y
of G. A k-level metric dimension refers to the minimum size of a fault-tolerant resolving set with the tolerance level k. In this article, we calculate and determine the k-level metric dimension for the circulant graph C(n:1,2)
for all possible values of k and n.
The optimal fault-tolerant resolving sets with k tolerance are also delineated.
Original languageEnglish
Article number1896
Pages (from-to)1-16
Number of pages16
JournalMathematics
Volume11
Issue number8
DOIs
Publication statusPublished - 17 Apr 2023

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