Skip to main content
SpringerLink
Log in

On Exclusive Sum Labellings of Hypergraphs

  • Original Paper
  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

The class \({\mathcal {E}}_k\) of hypergraphs with a k-exclusive sum labelling is hereditary, but non-trivial to characterise even for \(k=1\). Our main result is a complete description of the minimal forbidden induced subhypergraphs of \({\mathcal {E}}_1\) that are 3-uniform with maximum vertex degree 2. We also show that every hypertree has a 1-exclusive sum labelling and every combinatorial design does not.

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

Similar content being viewed by others

References

  1. Gallian, J.A.: A dynamic survey of graph labeling. Electron. J. Combin. 1, DS6 (2018) (DynamicSurveys)

  2. Harary, F.: Sum graphs and difference graphs. Congr. Numer. 72, 101–108 (1990)

    MathSciNet  MATH  Google Scholar 

  3. Miller, M., Patel, D., Ryan, J., Sugeng, K., Slamin, Tuga, M.: Exclusive sum labeling of graphs. JCMCC 55, 149–158 (2005)

    MathSciNet  MATH  Google Scholar 

  4. Miller, M., Ryan, J., Ryjáček, Z.: Characterisation of graphs with exclusive sum labelling. Australas. J. Comb. 69(3), 334–348 (2017)

    MathSciNet  MATH  Google Scholar 

  5. Ryan, J.: Exclusive sum labeling of graphs: a survey. AKCE Int. J. Graphs Comb. 6(1), 113–126 (2009)

    MathSciNet  MATH  Google Scholar 

  6. Sonntag, M., Teichert, H.-M.: Some results on exclusive sum labelings of hypergraphs. Graphs Combin. 31(6), 2401–2412 (2015)

    Article  MathSciNet  Google Scholar 

  7. Stinson, D.: Combinatorial Designs: Constructions and Analysis. Springer, New York (2004). https://link.springer.com/book/10.1007/b97564

    MATH  Google Scholar 

  8. Teichert, H.-M.: The sum number of d-partite complete hypergraphs. Discussiones Mathematicae Graph Theory 19(1), 79–91 (1999)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of West Bohemia, Pilsen, Czech Republic

    Christopher Purcell

  2. School of Electrical Engineering and Computer Science, The University of Newcastle, Callaghan, NSW, 2308, Australia

    Joe Ryan

  3. European Centre of Excellence NTIS, Department of Mathematics, University of West Bohemia, Pilsen, Czech Republic

    Zdeněk Ryjáček & Mária Skyvová

Authors
  1. Christopher Purcell
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joe Ryan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zdeněk Ryjáček
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mária Skyvová
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christopher Purcell.

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

Purcell, C., Ryan, J., Ryjáček, Z. et al. On Exclusive Sum Labellings of Hypergraphs. Graphs and Combinatorics 38, 46 (2022). https://doi.org/10.1007/s00373-021-02432-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00373-021-02432-4

Keywords

Search

Navigation