Skip to main content
SpringerLink
Log in

b-Coloring of the Mycielskian of Regular Graphs

  • Conference paper
  • First Online:
Algorithms and Discrete Applied Mathematics (CALDAM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11394))

Included in the following conference series:

  • 584 Accesses

Abstract

The b-chromatic number b(G) of a graph G is the maximum k for which G has a proper vertex coloring using k colors such that each color class contains at least one vertex adjacent to a vertex of every other color class. In this paper, we have mainly investigated on the b-chromatic number of the Mycielskian of regular graphs. In particular, we have obtained the exact value of the b-chromatic number of the Mycielskian of some classes of graphs. This includes a few families of regular graphs, graphs with \(b(G)=2\) and split graphs. In addition, we have found bounds for the b-chromatic number of the Mycielskian of some more families of regular graphs in terms of the b-chromatic number of their original graphs.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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. Balakrishnan, R., Kavaskar, T.: b-coloring of Kneser graphs. Discret. Appl. Math. 160(1–2), 9–14 (2012)

    Article  MathSciNet  Google Scholar 

  2. Balakrishnan, R., Raj, S.F.: Bounds for the b-chromatic number of the Mycielskian of some families of graphs. Ars Comb. 122, 89–96 (2015)

    MathSciNet  MATH  Google Scholar 

  3. Balakrishnan, R., Raj, S.F., Kavaskar, T.: b-coloring of Cartesian product of odd graphs. Ars Comb. 131, 285–298 (2017)

    MathSciNet  MATH  Google Scholar 

  4. Francis, P., Raj, S.F.: On b-coloring of powers of hypercubes. Discret. Appl. Math. 225, 74–86 (2017)

    Article  MathSciNet  Google Scholar 

  5. Hall, P.: On representatives of subsets. J. London Math. Soc. 1(1), 26–30 (1935)

    Article  Google Scholar 

  6. Irving, R.W., Manlove, D.F.: The b-chromatic number of a graph. Discret. Appl. Math. 91(1–3), 127–141 (1999)

    Article  Google Scholar 

  7. Kouider, M.: b-chromatic number of a graph, subgraphs and degrees. Rapport interne LRI 1392 (2004)

    Google Scholar 

  8. Kouider, M., El Sahili, A.: About b-colouring of regular graphs. Rapport de Recherche 1432 (2006)

    Google Scholar 

  9. Kratochvíl, J., Tuza, Z., Voigt, M.: On the b-chromatic number of graphs. In: Goos, G., Hartmanis, J., van Leeuwen, J., Kučera, L. (eds.) WG 2002. LNCS, vol. 2573, pp. 310–320. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-36379-3_27

    Chapter  Google Scholar 

  10. Mycielski, J.: Sur le coloriage des graphs. Colloq. Math. 3(2), 161–162 (1955)

    Article  MathSciNet  Google Scholar 

  11. West, D.B.: Introduction to Graph Theory. Prentice-Hall of India Private Limited, Delhi (2005)

    MATH  Google Scholar 

Download references

Acknowledgment

For the first author, this research was supported by SERB DST Project, Government of India, File no: EMR/2016/007339. For the second author, this research was supported by UGC - BSR, Research Fellowship, Government of India.

Author information

Authors and Affiliations

  1. Department of Mathematics, Pondicherry University, Puducherry, 605014, India

    S. Francis Raj & M. Gokulnath

Authors
  1. S. Francis Raj
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Gokulnath
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Francis Raj .

Editor information

Editors and Affiliations

  1. Indian Institute of Technology, Kharagpur, India

    Sudebkumar Prasant Pal

  2. Cochin University of Science and Technology, Cochin, India

    Ambat Vijayakumar

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Francis Raj, S., Gokulnath, M. (2019). b-Coloring of the Mycielskian of Regular Graphs. In: Pal, S., Vijayakumar, A. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2019. Lecture Notes in Computer Science(), vol 11394. Springer, Cham. https://doi.org/10.1007/978-3-030-11509-8_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-11509-8_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11508-1

  • Online ISBN: 978-3-030-11509-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation