Skip to main content

A Note on a Problem of L. Martínez on Almost-Uniform Partial Sum Families

  • Conference paper
  • First Online:
Isomorphisms, Symmetry and Computations in Algebraic Graph Theory (WAGT 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 305))

  • 607 Accesses

Abstract

It is known that there is a close relation between directed strongly regular graphs and partial sum families. In this short note, we construct some partial sum families from known directed strongly regular graphs. As a byproduct, we give a partial answer to a question posed by Martínez in [4].

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. A. Araluze, I. Kovács, K. Kutnar, L. Martínez, D. Marušič, Partial sum quadruples and bi-Abelian digraphs. J. Combin. Theory Ser. A 119, 1811–1831 (2012)

    Article  MathSciNet  Google Scholar 

  2. A.M. Duval, A directed graph version of strongly regular graphs. J. Combin. Theory Ser. A 47, 71–100 (1988)

    Article  MathSciNet  Google Scholar 

  3. GAP - Groups, Algorithms, Programming - a System for Computational Discrete Algebra, https://www.gap-system.org

  4. L. Martínez, Strongly regular \(m\)-Cayley circulant graphs and digraphs. Ars Mathem. Contemporanea 8, 195–213 (2015)

    Article  MathSciNet  Google Scholar 

  5. L. Martínez, A. Araluze, New tools for construction of directed strongly regular digraphs: difference digraphs and partial sum families. J. Combin. Theory Ser. B 100, 720–728 (2010)

    Article  MathSciNet  Google Scholar 

  6. O. Olmez, S.Y. Song, Some families of directed strongly regular graphs obtained from certain finite incidence structures. Graphs Combin. 30, 1529–1549 (2014)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The author gratefully acknowledges the contribution of the Scientific Grant Agency of Slovak Republic under the grant VEGA 1/0988/16 and the contribution of the Slovak Research and Development Agency under the projects APVV-0136-12 and APVV-0220-15.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Štefan Gyürki .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Gyürki, Š. (2020). A Note on a Problem of L. Martínez on Almost-Uniform Partial Sum Families. In: Jones, G., Ponomarenko, I., Širáň, J. (eds) Isomorphisms, Symmetry and Computations in Algebraic Graph Theory. WAGT 2016. Springer Proceedings in Mathematics & Statistics, vol 305. Springer, Cham. https://doi.org/10.1007/978-3-030-32808-5_3

Download citation

Publish with us

Policies and ethics