Skip to main content
SpringerLink
Log in

Realizing unit graphs associated with rings

  • Published:
Afrika Matematika Aims and scope Submit manuscript

Abstract

Let R be a commutative ring with a non-zero identity. The unit graph of R, denoted by G(R), is a simple graph obtained by setting all the elements of R to be the vertices and two distinct vertices x and y are adjacent if and only if \(x + y\) is a unit of R. In this paper, we determine the classes of graphs which can be realized as a unit graph. Further, we have made an amendment in the Theorem 3.5 (Ashrafi et al. in Commun Algebra 38:2851–2871, 2010).

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

Similar content being viewed by others

References

  1. Ashrafi, N., Maimani, H.R., Pournaki, M.R., Yassemi, S.: Unit graphs associated with rings. Commun. Algebra 38, 2851–2871 (2010)

    Article  MathSciNet  Google Scholar 

  2. Grimaldi, R.P.: Graphs from rings. In: Proceedings of the Twentieth Southeastern conference on combinatorics. Graph Theory Comput. Congr. Numer. 71, 95–103 (1990)

  3. Harary, F.: Graph Theory. Addison-Wesley Publ. Comp. Inc, California, MA (1969)

  4. Jacobson, N.: Lectures in Abstract Algebra. East-West Press P. Ltd, New Delhi (1951)

    MATH  Google Scholar 

  5. Maimani, H.R., Pournaki, M.R., Yassemi, S.: Rings which are generated by their units: a graph theoretical approach. Elem. Math. 65, 17–25 (2010)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors express their gratitude to anonymous referees for careful reading of the manuscript and for providing valuable suggestions.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Rajasthan, JLN Marg, Jaipur, 302004, India

    Pranjali

  2. Department of Mathematics and Statistics, Banasthali Vidyapith, Banasthali, Rajasthan, 304022, India

    Amit Kumar & Saumya Bhadauriya

Authors
  1. Pranjali
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amit Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Saumya Bhadauriya
    View author publications

    You can also search for this author in PubMed Google Scholar

Ethics declarations

Conflicts of interest

Authors do not have conflicts of interest.

Additional information

Publisher's Note

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

This paper is dedicated on the 68th birthday of Dr. Mukti Acharya [Former Head and Professor, Department of Applied Mathematics, Delhi Technological University Delhi-110042, India]

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pranjali, Kumar, A. & Bhadauriya, S. Realizing unit graphs associated with rings. Afr. Mat. 33, 33 (2022). https://doi.org/10.1007/s13370-022-00966-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13370-022-00966-1

Keywords

Mathematics Subject Classification

Search

Navigation