Skip to main content
SpringerLink
Log in

The locating number of hexagonal Möbius ladder network

  • Original Research
  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

Due to the immense applications of interconnection networks, various new networks are designed and extensively used in computer sciences and engineering fields. Networks can be expressed in the form of graphs, where node become vertex and links between nodes are called edges. To obtain the exact location of a specific node which is unique from all the nodes, several nodes are selected this is called locating/resolving set. Minimum number of nodes in the locating set is called locating number. In this article, we find the exact value of locating number of newly designed hexagonal Möbius ladder network.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Aiazzi, B., Baronti, S., Capanni, A., Santurri, L., Vitulli, R.: Advantages of hexagonal sampling grids and hexagonal shape detector elements in remote sensing imagers. In: 2002 11th European Signal Processing Conference, pp. 1–4. IEEE (2002)

  2. Ali, M., Ali, G., Imran, M., Baig, A.Q., Shafiq, M.K.: On the metric dimension of Möbius ladders. Ars Combin. 105, 403–410 (2012)

    MathSciNet  MATH  Google Scholar 

  3. Birch, C.P.D., Oom, S.P., Beecham, J.A.: Rectangular and hexagonal grids used for observation, experiment and simulation in ecology. Ecol. Modell. 206(3–4), 347–359 (2007)

    Article  Google Scholar 

  4. Chartrand, G., Eroh, L., Johnson, M.A., Oellermann, O.R.: Resolvability in graphs and the metric dimension of a graph. Discrete Appl. Math. 105(1–3), 99–113 (2000)

    Article  MathSciNet  Google Scholar 

  5. Chartrand, G., Saenpholphat, V., Zhang, P.: The independent resolving number of a graph. Math. Bohem. 128, 379–393 (2003)

    Article  MathSciNet  Google Scholar 

  6. Davis, R.L.: U.S. Patent No. 3,267,406. U.S. Patent and Trademark Office, Washington, DC (1996)

  7. Harary, F., Melter, R.A.: On the metric dimension of a graph. Ars Combin. 2, 191–195 (1976)

    MathSciNet  MATH  Google Scholar 

  8. Hauptmann, M., Schmied, R., Viehmann, C.: Approximation complexity of metric dimension problem. J. Discrete Algoritms 14, 214–222 (2012)

    Article  MathSciNet  Google Scholar 

  9. Khuller, S., Raghavachari, B., Rosenfeld, A.: Landmarks in graphs. Discrete Appl. Math. 70(3), 217–229 (1996)

    Article  MathSciNet  Google Scholar 

  10. Kumar, B., Gupta, P., Pahwa, K.: Square pixels to hexagonal pixel structure representation technique. Int. J. Signal Process. Image Process. Pattern Recognit. 7(4), 137–144 (2014)

    Google Scholar 

  11. Lewis, H.R., Garey, M.R., Johnson, D.S.: Computers and intractability. A guide to the theory of NP-completeness. W.H. Freeman and Company, San Franciscoc (1979). J. Symb. Log. 48(2), 498–500 (1983)

  12. Lukin, O., Vogtle, F.: Knotting and threading of molecules: chemistry and chirality of molecular knots and their assemblies. Angew. Chem. 44(10), 1456–1477 (2005)

    Article  Google Scholar 

  13. Manthey, R., Schlosser, T., Kowerko, D.: Generation of images with hexagonal tessellation using common digital cameras. In: IBS International Summer School on Computer Science. Computer Engineering and Education Technology (2017)

  14. Manuel, P.D., Rajan, B., Rajasingh, I., Monica, M.C.: On minimum metric dimension of honeycomb networks. J. Discrete Algorithm 6, 20–27 (2008)

    Article  MathSciNet  Google Scholar 

  15. Mocnik, F.-B.: A novel identifier scheme for the ISEA Aperture 3 Hexagon Discrete Global Grid System. Cartogr. Geogr. Inf. Sci. 46(3), 277–291 (2018)

    Article  Google Scholar 

  16. Perez-Enriquez, R.: A structural parameter for high TC superconductivity from an octahedral Möbius strip in RBaCuO: 123 type perovskites. R. arXiv:cond-mat/0308019 (2003)

  17. Pond, J.M.: Mobius dual-mode resonators and bandpass filters. IEEE Trans. Microw. Theory Technol. 48(12), 2465–2471 (2000)

    Article  Google Scholar 

  18. Rohde, U.L., Poddar, A.K., Sundararajan, D.: Printed resonators: mobius strip theory and applications. Microw. J. 56(11), 24 (2013)

    Google Scholar 

  19. Sahr, K., White, D., Kimerling, A.J.: Geodesic discrete global grid systems. Cartogr. Geogr. Inf. Sci. 30(2), 121–134 (2003)

    Article  Google Scholar 

  20. Sebő, A., Tannier, E.: On metric generators of graphs. Math. Oper. Res. 29(2), 383–393 (2004)

    Article  MathSciNet  Google Scholar 

  21. Shao, Z., Wu, P., Zhu, E., Chen, L.: On metric dimension in some hex derived networks. Sensors 19(1), 94 (2018)

    Article  Google Scholar 

  22. Siddiqui, H.M.A., Imran, M.: Computing the metric dimension of wheel related graphs. Appl. Math. Comput. 242, 624–632 (2014)

    MathSciNet  MATH  Google Scholar 

  23. Slater, P.J.: Leaves of trees. Congr. Numer. 14, 549–559 (1975)

    MathSciNet  MATH  Google Scholar 

  24. Söderberg, S., Shapiro, H.S.: A combinatory detection problem. Am. Math. Mon. 70(10), 1066–1070 (1963)

    Article  MathSciNet  Google Scholar 

  25. Wen, W., Khatibi, S.: Virtual deformable image sensors: towards to a general framework for image sensors with flexible grids and forms. Sensors 18(6), 1856 (2018)

    Article  Google Scholar 

  26. Yamashiro, A., Shimoi, Y., Harigaya, K., Wakabayashi, K.: Novel electronic states in graphene ribbons-competing spin and charge orders. Physica E 22(1–3), 688–691 (2004)

    Article  Google Scholar 

Download references

Acknowledgements

The authors are very grateful to the reviewers for their careful reading with corrections, suggestions and useful comments.

Author information

Authors and Affiliations

  1. Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, 54000, Pakistan

    Muhammad Faisal Nadeem & Adnan Khalil

  2. Department of Aerospace Engineering, Faculty of Engineering, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia

    Muhammad Azeem

Authors
  1. Muhammad Faisal Nadeem
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Muhammad Azeem
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Adnan Khalil
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Faisal Nadeem.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nadeem, M.F., Azeem, M. & Khalil, A. The locating number of hexagonal Möbius ladder network. J. Appl. Math. Comput. 66, 149–165 (2021). https://doi.org/10.1007/s12190-020-01430-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-020-01430-8

Keywords

Mathematics Subject Classification

Search

Navigation