# On the (2,2)-domination number of trees

You Lu; Xinmin Hou; Jun-Ming Xu

Discussiones Mathematicae Graph Theory (2010)

- Volume: 30, Issue: 2, page 185-199
- ISSN: 2083-5892

## Access Full Article

top## Abstract

top## How to cite

topYou Lu, Xinmin Hou, and Jun-Ming Xu. "On the (2,2)-domination number of trees." Discussiones Mathematicae Graph Theory 30.2 (2010): 185-199. <http://eudml.org/doc/271068>.

@article{YouLu2010,

abstract = {Let γ(G) and $γ_\{2,2\}(G)$ denote the domination number and (2,2)-domination number of a graph G, respectively. In this paper, for any nontrivial tree T, we show that $(2(γ(T)+1))/3 ≤ γ_\{2,2\}(T) ≤ 2γ(T)$. Moreover, we characterize all the trees achieving the equalities.},

author = {You Lu, Xinmin Hou, Jun-Ming Xu},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {domination number; total domination number; (2,2)-domination number; -domination number},

language = {eng},

number = {2},

pages = {185-199},

title = {On the (2,2)-domination number of trees},

url = {http://eudml.org/doc/271068},

volume = {30},

year = {2010},

}

TY - JOUR

AU - You Lu

AU - Xinmin Hou

AU - Jun-Ming Xu

TI - On the (2,2)-domination number of trees

JO - Discussiones Mathematicae Graph Theory

PY - 2010

VL - 30

IS - 2

SP - 185

EP - 199

AB - Let γ(G) and $γ_{2,2}(G)$ denote the domination number and (2,2)-domination number of a graph G, respectively. In this paper, for any nontrivial tree T, we show that $(2(γ(T)+1))/3 ≤ γ_{2,2}(T) ≤ 2γ(T)$. Moreover, we characterize all the trees achieving the equalities.

LA - eng

KW - domination number; total domination number; (2,2)-domination number; -domination number

UR - http://eudml.org/doc/271068

ER -

## References

top- [1] T.J. Bean, M.A. Henning and H.C. Swart, On the integrity of distance domination in graphs, Australas. J. Combin. 10 (1994) 29-43. Zbl0815.05036
- [2] G. Chartrant and L. Lesniak, Graphs & Digraphs (third ed., Chapman & Hall, London, 1996).
- [3] M. Fischermann and L. Volkmann, A remark on a conjecture for the (k,p)-domination number, Utilitas Math. 67 (2005) 223-227. Zbl1077.05074
- [4] M.A. Henning, Trees with large total domination number, Utilitas Math. 60 (2001) 99-106. Zbl1011.05045
- [5] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (New York, Marcel Deliker, 1998). Zbl0890.05002
- [6] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics (New York, Marcel Deliker, 1998). Zbl0883.00011
- [7] T. Korneffel, D. Meierling and L. Volkmann, A remark on the (2,2)-domination number Discuss. Math. Graph Theory 28 (2008) 361-366, doi: 10.7151/dmgt.1411. Zbl1156.05044

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.