Fault-Tolerant Metric Dimension of Circulant Graphs

Laxman Saha, Rupen Lama, Kalishankar Tiwary, Kinkar Chandra Das and Yilun Shang
Additional contact information
Laxman Saha: Department of Mathematics, Balurghat College, Balurghat 733101, India
Rupen Lama: Department of Mathematics, Balurghat College, Balurghat 733101, India
Kalishankar Tiwary: Department of Mathematics, Raiganj University, Raiganj 733134, India
Kinkar Chandra Das: Department of Mathematics, Sungkyunkwan University, Suwon 16419, Korea
Yilun Shang: Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK

Mathematics, 2022, vol. 10, issue 1, 1-16

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 = { s 1 , s 2 , … , s k } ⊂ V ( G ) is called a resolving set for G if, for any two distinct vertices u , v ∈ V ( G ) , there is a vertex s i ∈ S such that d ( u , s i ) ≠ d ( v , s i ) . 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 C n ( 1 , 2 , 3 ) has determined the exact value of β ′ ( C n ( 1 , 2 , 3 ) ) . In this article, we extend the results of Basak et al. to the graph C n ( 1 , 2 , 3 , 4 ) and obtain the exact value of β ′ ( C n ( 1 , 2 , 3 , 4 ) ) for all n ≥ 22 .

Keywords: circulant graphs; resolving set; fault-tolerant resolving set; fault-tolerant metric dimension (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/1/124/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/1/124/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:1:p:124-:d:716040

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().