ON METRIC DIMENSION OF PIBRENTASVIR AND VANCOMYCIN
Ajay Kumar Sharma
Department of Mathematics,
Government Degree College,
Udhampur-182101, Jammu and Kashmir, India

Abstract

Let ζ = (V,E) be a nth order connected graph. If the distance vectors to the vertices in an ordered subset Hr of vertices can uniquely identify each vertex of the graph ζ, then the set Hr is known as resolving set for the graph ζ. The resolving set Hr with smallest cardinality serves as the metric dimension of graph ζ and this resolving set serves as the metric basis for ζ. Since very early times, medicinal drugs have played a significant part in human civilization. In this article, we study the metric dimension for the typical molecular structures of two important drugs namely pibrentasvir (P80) and vancomycin (V101). MSC(2020): 05C10, 05C12, 68R10.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 35
Issue: 6
Year: 2022

Download Section



Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

  1. [1] A.N. Koam and A. Ahmad Barycentric subdivision of Cayley graphs with constant edge metric dimension, IEEE Access 3 (2020) 80624–80628. https://doi.org/10.1109/ACCESS.2020.2990109.
  2. [2] A. Kelenc, D. Kuziak, A. Taranenko and I.G. Yero, Mixed metric dimension of graphs, Appl. Math. Comput. 314 (2017) 429–438. https://doi.org/10.1016/j.amc.2017.07.027
  3. [3] A. Kelenc, N. Tratnik and I.G. Yero, Uniquely identifying the edges of a graph: the edge metric dimension, Discret. Appl. Math. 31 (2018) 204–220. https://doi.org/10.1016/j.dam.2018.05.052.
  4. [4] A. Seb˜o and E. Tannier, On metric generators of graphs, Math. Oper.Res., 29(2) (2004) 383–393.
  5. [5] B.H. Xing, S.K. Sharma, V.K. Bhat, H. Raza and J.B. Liu, The vertex edge resolvability of some wheel-related graphs, J Math 1859714 (2021). https://doi.org/10.1155/2021/1859714
  6. [6] B. Yang, M. Rafullah, H.M.A. Siddiqui and S. Ahmad, On resolvability parameters of some wheelrelated graphs, J Chem 9259032 (2019). https://doi.org/10.1155/2019/9259032
  7. [7] F. Harary and R. A. Melter, On the metric dimension of a graph, Ars Comb. 2 (1976), 191-195.
  8. [8] F. Simonraj and A. George, On the metric dimension of silicate stars, ARPN J. Eng. Appl. Sci. 5 (2015) 2187–2192.
  9. [9] G. Chartrand, L. Eroh, M.A Johnson and O.R Oellermann, Resolvability in graphs and the metric dimension of a graph, Discrete Appl. Math. 105 (2000) 99–113. https://doi.org/10.1016/S0166218X(00)00198-0.
  10. [10] G. Chartrand, V. Saenpholphat and P. Zhang, The independent resolving number of a graph, Math. Bohem. 128 (2003) 379–393.
  11. [11] H.M. Siddiqui and M. Imran, Computing the metric and partition dimension of H-Naphtalenic and VC5C7 nanotubes, J. Optoelectron Adv. Mater.7(5) (2015) 790–794.
  12. [12] I. Javaid, M. T. Rahim and K. Ali, Families of regular graphs with constant metric dimension, Util. Math. 75 (2008) 21-34.
  13. [13] K. Liu, and N. Abu-Ghazaleh, Virtual coordinate back tracking for void travarsalin geographic routing, In International Conference on Ad-Hoc Networks and Wireless,Springer, Berlin, Heidelberg 4104 (2006), 46-59.
  14. [14] Y. N. Lamb, Glecaprevir/pibrentasvir: first global approval, Drugs 77(16) (2017) 1797-1804.
  15. [15] M. Ahsan, Z. Zahid, S. Zafar, A. Rafq, M.S. Sindhu and M. Umar, Computing the edge metric dimension of convex polytopes related graphs, J Math Computer Sci 22 (2021) 174–188. https://doi.org/10.22436/jmcs.022.02.08.
  16. [16] P. J. Slater, Leaves of trees, Proc. 6th Southeastern Conf. Combinatorics, Graph Theory, Comput., Congressus Numerantium, The Netherlands,14 (1975) 549–559.
  17. [17] M. Imran, S. A. Bokhary and A. Q. Baig, Families of Rotationally-Symmetric Plane Graphs with Constant Metric Dimension, Southeast Asian Bull. Math. 36 (2012), 663-675.
  18. [18] N. Trinajstic, Chemical graph theory, Routledge World Health Organization (2000) Air quality guidelines for Europe. Copenhagen: World Health Organization, Regional Office for Europe. (2018)https://apps.who.int/iris/handle/10665/107335.
  19. [19] P. Erdos and A. R´enyi, On two problems of information theory, Magyar Tud. Akad. Mat. Kutat´o Int. K¨ozl 8 (1963) 229-243.
  20. [20] R.A. Melter and I. Tomescu, Metric bases in digital geometry, Comput. Gr. Image Process 25 (1984)113–121. https://doi.org/10.1016/0734-189X(84)90051-3.
  21. [21] R.C. Tillquist, R.M. Frongillo and M.E. Lladser, Getting the lay of the land in discrete space: A survey of metric dimension and its applications, (2021) arXiv preprint arXiv:2104.07201.
  22. [22] V. Chvatal, Mastermind, Combinatorica 3(3) (1983), 325–329. https://doi.org/10.1007/BF02579188.
  23. [23] S. Khuller, B. Raghavachari and A. Rosenfeld, Landmarks in graphs, Disc. Appl. Math., 70 (1996) 217–229.
  24. [24] S.K. Sharma, H. Raza and V.K. Bhat, Computing edge metric dimension of one-pentagonal carbon nanocone, Front Phys 600 (2021). https://doi.org/10.3389/fphy.2021.749166.
  25. [25] S.K. Sharma and V.K. Bhat Metric dimension of heptagonal circular ladder, Discrete Math Algorithms Appl. 13(1):2050095. https://doi.org/10.1142/S1793830920500950.
  26. [26] Z. Beerliova, F. Eberhard, T. Erlebach, A. Hall, M. Hoffman, M. Mihalak and L. S. Ram, Network discovery and verification, IEEE J. Sel. Areas Commun. 24 (2006), 2168-2181.
  27. [27] Z. Hussain, M. Munir, A. Ahmad, M. Chaudhary, J.A Khan and I. Ahmed, Metric basis and metric dimension of 1-pentagonal carbon nanocone networks, Sci Rep 10(1) (2020) 1–7. https://doi.org/10.1038/s41598-020-76516-1.
  28. [28] Z. Raza and M.S. Bataineh The comparative analysis of metric and edge metric dimension of some subdivisions of the wheel graph, Asian Eur. J. Math 14(4) (2020) 2150062. https://doi.org/10.1142/S1793557121500625.