Fault-Tolerant Metric Dimension of Circulant Graphs

Saha, Laxman, Lama, Rupen, Tiwary, Kalishankar, Das, Kinkar Chandra and Shang, Yilun (2022) Fault-Tolerant Metric Dimension of Circulant Graphs. Mathematics, 10 (1). e124. ISSN 2227-7390

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Official URL: https://doi.org/10.3390/math10010124


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.

Item Type: Article
Additional Information: Funding information: L. Saha is supported by Science and Research Board (SERB), DST, India (Grant No. CRG/2019/006909). K. C. Das is supported by National Research Foundation funded by the Korean government (Grant No. 2021R1F1A1050646).
Uncontrolled Keywords: circulant graphs, resolving set, fault-tolerant resolving set, fault-tolerant metric dimension
Subjects: G100 Mathematics
G400 Computer Science
G900 Others in Mathematical and Computing Sciences
Department: Faculties > Engineering and Environment > Computer and Information Sciences
Depositing User: Rachel Branson
Date Deposited: 05 Jan 2022 12:08
Last Modified: 05 Jan 2022 12:15
URI: http://nrl.northumbria.ac.uk/id/eprint/48078

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