Skip to main content
SpringerLink
Log in

A note on the annihilation number and 2-domination number of a tree

Journal of Combinatorial Optimization volume 33, pages 968–976 (2017)Cite this article

Abstract

In 2014, Desormeaux et al. (Discrete Math 319:15–23, 2014) proved a relationship between the annihilation number and 2-domination number of a tree. In this note, we provide a family of bounds for the 2-domination number of a tree based on the amount of vertices of small degree. This family of bounds extends current bounds on the 2-domination number of a tree, and provides an alternative proof for the relationship between the annihilation number and the 2-domination number of a tree that was shown by Desormeaux et al.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

39,95 €

Price includes VAT (Finland)

References

  • Blidia M, Chellali M, Favaron O (2005) Independence and 2-domination in trees. Australas J Combin 33:317–327

    MathSciNet  MATH  Google Scholar 

  • Caro Y, Pepper R (2014) Degree sequence index strategy. Australas J Combin 59:1–23

    MathSciNet  MATH  Google Scholar 

  • Caro Y, Roditty Y (1990) A note on the \(k\)-domination number of a graph. Internat J Math Math Sci 13(1):205–206

  • Chellali M, Favaron O, Hansberg A, Volkmann L (2012) \(k\)-domination and \(k\)-independence in graphs: a survey. Graphs Combin 28(1):1–55

    Article  MathSciNet  MATH  Google Scholar 

  • DeLaViña E (2005) Written on the wall II, (conjectures of graffiti.pc). http://cms.uhd.edu/faculty/delavinae/research/wowii. Accessed August 10, 2015

  • DeLaViña E, Larson CE, Pepper R, Waller B (2010) Graffiti.pc on the 2-domination number of a graph. In: Proceedings of the forty-first southeastern international conference on combinatorics, graph theory and computing, vol 203, pp 15–32

  • Desormeaux WJ, Haynes TW, Henning MA (2013) Relating the annihilation number and the total domination number of a tree. Discrete Appl Math 161(3):349–354

    Article  MathSciNet  MATH  Google Scholar 

  • Desormeaux WJ, Henning MA, Rall DF, Yeo A (2014) Relating the annihilation number and the 2-domination number of a tree. Discrete Math 319:15–23

    Article  MathSciNet  MATH  Google Scholar 

  • Hansberg A, Meierling D, Volkmann L (2011) Independence and \(k\)-domination in graphs. Int J Comput Math 88(5):905–915

    Article  MathSciNet  MATH  Google Scholar 

  • Haynes TW, Hedetniemi ST, Slater PJ (1998) Fundamentals of domination in graphs, vol 208., Monographs and textbooks in pure and applied mathematicsMarcel Dekker Inc, New York

    MATH  Google Scholar 

  • Patterson SC (2015) 2-Domination and annihilation numbers. ProQuest LLC, Ann Arbor, thesis (Undergraduate Honors)–University of Southern Mississippi

  • Pepper R (2010) Implications of some observations about the \(k\)-domination number. In: Proceedings of the forty-first southeastern international conference on combinatorics, graph theory and computing, vol 206, pp 65–71

  • Pepper RD (2004) Binding independence. ProQuest LLC, Ann Arbor, thesis (Ph.D.)–University of Houston

Download references

Author information

Author notes

  1. Jeremy Lyle

    Present address: Olivet Nazarene University, Bourbonnais, IL, USA

Authors and Affiliations

  1. The University of Southern Mississippi, Hattiesburg, MS, USA

    Jeremy Lyle & Sean Patterson

Authors
  1. Jeremy Lyle
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sean Patterson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jeremy Lyle.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lyle, J., Patterson, S. A note on the annihilation number and 2-domination number of a tree. J Comb Optim 33, 968–976 (2017). https://doi.org/10.1007/s10878-016-0019-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10878-016-0019-7

Keywords

  • Annihilation number
  • 2-Domination number
  • Trees

Mathematics Subject Classification

  • 05C35

Search

Navigation