Fault-Tolerant Metric Dimension of Circulant Graphs

Laxman Saha, Rupen Lama, Kalishankar Tiwary, Kinkar Chandra Das*, Yilun Shang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
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Abstract

Let G be a connected graph with vertex set V(G) and d(u, v) be the distance between the vertices u and v. A set of vertices S={s1, s2, …, sk}⊂V(G) is called a resolving set for G if, for any two distinct vertices u, v∈V(G), there is a vertex si∈S such that d(u, si)≠d(v, si). A resolving set S for G is fault-tolerant if S∖{x} is also a resolving set, for each x in S, and the fault-tolerant metric dimension of G, denoted by β′(G), is the minimum cardinality of such a set. The paper of Basak et al. on fault-tolerant metric dimension of circulant graphs Cn(1, 2, 3) has determined the exact value of β′(Cn(1, 2, 3)). In this article, we extend the results of Basak et al. to the graph Cn(1, 2, 3, 4) and obtain the exact value of β′(Cn(1, 2, 3, 4)) for all n≥22.
Original languageEnglish
Article numbere124
Number of pages16
JournalMathematics
Volume10
Issue number1
DOIs
Publication statusPublished - 1 Jan 2022

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