KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2025 / Volume: 54 Issue: 6

Fault tolerant metric resolvability of convex polytopes

Asım Nadeem(Forman Christian College)0000-0002-0568-1592
Kamran Azhar(Forman Christian College)0000-0002-3584-9085
Agha Kashif(University of Management and Technology (UMT))0000-0002-1097-3450
Sohail Zafar(University of Management and Technology (UMT))0000-0002-8177-7799
Sayfa
—
Yayın Tarihi
2025-12-30
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The applications of FTMD have also been considered in the manuscript.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:Fault tolerant metric basis assigns a unique code in terms of distances to each node of the graph which works in the presence of faults.
📊
Temel Bulgular & Veri:The distance based parameters are widely used in different fields like robot navigation, interconnection networks, sensor deployments, image processing and chemistry.
💡
Sonuç & Katkı:The applications of FTMD have also been considered in the manuscript.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:convex polytopes · metric dimension · fault tolerant metric dimension

Abstract

Fault tolerant metric basis assigns a unique code in terms of distances to each node of the graph which works in the presence of faults. The distance based parameters are widely used in different fields like robot navigation, interconnection networks, sensor deployments, image processing and chemistry. The convex polytopes are stable and destroy resistant which make them attractive choice for interconnection networks and anti-tracking networks. The current article, computes the fault tolerant metric dimension (FTMD) of convex polytopes $B_n, C_n, E_n$ and $U_n$. The applications of FTMD have also been considered in the manuscript.

🔖

Bu Makaleye Atıf Yap

Nadeem, A., Azhar, K., Kashif, A., Zafar, S. (2025). Fault tolerant metric resolvability of convex polytopes. Hacettepe Journal of Mathematics and Statistics, Volume: 54 Issue: 6. https://doi.org/10.15672/hujms.1336986

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (22)

  1. S. Akhter and R. Farooq, Metric dimension of fullerene graphs, EJGTA. 7 (1), 91–103, 2019.
  2. H. Bashir, Z. Zahid, A. Kashif, S. Zafar and J.B. Liu, On 2-metric resolvability in rotationally-symmetric graphs, J. Intell. Fuzzy Syst. 40 (6), 11887–11895, 2021.
  3. G. Chartrand and P. Zhang, The theory and applications of resolvability in graphs, A survey. Congr. Numer. 160, 47–68, 2003.
  4. A. Estrado-Moreno, J.A. Rodriguez-Velaquez and I.G. Yero, The k−metric dimension of a graph, Appl. Math. Inf. Sci. 9 (6), 2829–2840, 2015.
  5. M.R. Garey and D.S. Johnson, Computers and intractability: a guide to the theory of NP-completeness, Freeman, New York, 1979.
  6. C. Hernando, M. Mora, P.J. Slater and D.R. Wood, Fault-tolerant metric dimension of graphs, In proceedings international conference on convexity in Discrete Structures; Ramanujan Mathematical Society: Tiruchirappalli, India, 5, 81–85, 2008.
  7. Z. Hussain and M.M. Munir, Fault-tolerance in metric dimension of boron nanotubes lattices, Front. Comput. Neurosci. 16, 1–12, 2023.
  8. M. Imran, A.Q. Baig, F. Bashir, A. Riasat, A.U.H. Bokhary, and I. Tomescu, On metric dimension of flower graphs and convex polytopes, Util. Math. 13 (92), 389–409, 2013.
  9. M. Imran, S.A.U.H. Bokhary, and A.Q. Baig, On families of convex polytopes with constant metric dimension, Comput. Math. with Appl. 60, 2629–2638, 2010.
  10. M. Imran, S.A.U.H. Bokhary, and A.Q. Baig, On the metric dimension of rotationally-symmetric convex polytopes, J. Algebra Comb. Discrete Appl. 3 (2), 45–59, 2015.
  11. I. Javaid, M. Salman, M.A. Chaudhry and S. Shokat, Fault tolerance in resolvability, Utilitas Mathematica. 80, 263–275, 2009.
  12. J.B. Liu, M.F. Nadeem and M. Azeem, Bounds on the partition dimension of convex polytopes, Comb. Chem. High Throughput Screen. 23, 1–13, 2020.
  13. N. Mehreen, R. Farooq and S. Akhter, On partition dimension of fullerene graphs, AIMS Mathematics, 3(3), 343–352, 2018.
  14. A. Nadeem, A. Kashif, E. Bonyah and S. Zafar, Fault tolerant partition resolvability in convex polytoes, Math. Probl. Eng. 2022, 1–12, 2022.
  15. H. Raza, S. Hayat and X.F. Pan, On the fault-tolerant metric dimension of convex polytopes, Appl. Math Comput. 339, 172–185, 2018.
  16. L. Saha, R. Lama, K. Tiwary, K. C. Das and Y. Shang, Fault-tolerant metric dimension of circulant graphs, Mathematics, 10 (124), 1–16, 2022.
  17. H.M.A. Siddiqui, S. Hayat, A. Khan, M. Imran, A. Razzaq, and J.B. Liu, Resolvability and fault-tolerant resolvability structures of convex polytopes, Theor. Comput. Sci. 796, 114–128, 2019.
  18. C. Tian, Y. Zhang and T. Yin, Modeling of anti-tracking network based on convexpolytope topology, In Computational ScienceICCS 2020: 20th International Conference, Amsterdam, The Netherlands, June 35, 2020, Proceedings, Part II 20 (pp. 425-438). Springer International Publishing.
  19. I.G. Yero, A. Estrado-Moreno and J.A. Rodríguez-Velázquez, Computing the k−metric dimension of graphs, Appl. Math. Comput. 300, 60–69, 2017.
  20. Z.B. Zheng, A. Ahmad, Z. Hussain, M. Munir, M.I. Qureshi, I. Ali and J.B. Liu, Fault-Tolerant Metric Dimension of Generalized Wheels and Convex Polytopes, Math. Probl. Eng. 2020, 1–8, 2020.
  21. M. Imran, S.A.U.H. Bokhary, and A.Q. Baig, On families of convex polytopes with constant metric dimension, Comput. Math. with Appl. 60, 2629–2638, 2010.
  22. M. Imran, S.A.U.H. Bokhary, and A.Q. Baig, On the metric dimension of rotationally-symmetric convex polytopes, J. Algebra Comb. Discrete Appl. 3 (2), 45–59, 2015.