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- Title
Computation of the Fault-Tolerant Metric Dimension of Certain Networks.
- Authors
Bashir, Humera; Zahid, Zohaib; Ojiema, Michael Onyango
- Abstract
The only thing that remains to show is HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi> </mi><mfenced open="(" close=")" separators="|"><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></mfenced><mo>/=</mo><mn>3</mn></math> ht . It is exclusively required to prove that HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi> </mi><mfenced open="(" close=")" separators="|"><mrow><mi>P</mi><mfenced open="(" close=")" separators="|"><mrow><mi>n</mi><mo>,</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>/=</mo><mn>3</mn></math> ht . Hence, in view of Lemma 2 together with the Theorem 1, we conclude that HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi> </mi><mfenced open="(" close=")" separators="|"><mrow><mi>P</mi><mfenced open="(" close=")" separators="|"><mrow><mi>n</mi><mo>,</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>=</mo><mn>4</mn></math> ht . Therefore, in lights of Lemma 3 combined with the Theorem 1, we conclude that HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi> </mi><mfenced open="(" close=")" separators="|"><mrow><mi>P</mi><mfenced open="(" close=")" separators="|"><mrow><mi>n</mi><mo>,</mo><mn>2</mn></mrow></mfenced></mrow></mfenced><mo>=</mo><mn>4</mn></math> ht .
- Subjects
PETERSEN graphs; ERROR-correcting codes; COMBINATORICS; METRIC spaces; REGULAR graphs
- Publication
Mathematical Problems in Engineering, 2022, p1
- ISSN
1024-123X
- Publication type
Article
- DOI
10.1155/2022/6385673