Skip to main content
SpringerLink
Log in

Vertex labeling of a half-cube to induce face labels in arithmetic progression

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

Abstract

A plane, passing through the center and orthogonal to a diagonal, slices a cube into two identical halves each having three triangles, three pentagons and a hexagon. If you label the ten vertices of a half-cube with numbers, then each face is said to receive an induced face label given by the sum of all vertices around it. Label the ten vertices of a half-cube with digits 0 through 9 so that the induced labels of the three triangles and the three pentagons constitute six consecutive multiples of a fixed number, or more generally six numbers in arithmetic progression.

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
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. C. J. Deeni and D. Antony Xavier, Super vertex magic and E-super vertex magic total labeling, Proceedings of the International Conference on Applied Mathematics and Theoretical Computer Science, (2013), 116–120.

  2. J. A. Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics, (2017) #DS6.

  3. Jack Gittinger, A plane intersecting a cube, GeoGebra: An Internet Resource. Retrieved on December 12, 2020 from https://www.geogebra.org/m/aY75dEkf.

  4. J. Sarkar, Magic-vertex labeling of a half-cube, Resonance, 25 (2020), no. 12, 1689-1703.

    Article  Google Scholar 

  5. J. Sarkar, Super odd-sum labeling of a cube: What an odd cube! Resonance, (2021) to appear.

  6. J. Sarkar, Vertex labeling of a half-cube to induce binary face labeling, International Journal of Mathematics, Statistics and Operations Research, accepted.

  7. V. Swaminathan and P. Jeyanthi, Super vertex magic labeling, Indian J. Pure Appl. Math., 34 (2003), no. 6, 935–939.

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This paper is a product to satisfy the curiosity of my students. Thanks are due to Professor George Gopen who, through his books and workshops, taught me how to write in a reader-centric style.

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N Blackford Street, Indianapolis, IN, 46202, USA

    Jyotirmoy Sarkar

Authors
  1. Jyotirmoy Sarkar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jyotirmoy Sarkar.

Additional information

Communicated by B. Sury.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sarkar, J. Vertex labeling of a half-cube to induce face labels in arithmetic progression. Indian J Pure Appl Math 53, 593–608 (2022). https://doi.org/10.1007/s13226-021-00151-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13226-021-00151-3

Keywords

Mathematics Subject Classification

Search

Navigation