# Total domination of Cartesian products of graphs

Discussiones Mathematicae Graph Theory (2007)

- Volume: 27, Issue: 1, page 175-178
- ISSN: 2083-5892

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topXinmin Hou. "Total domination of Cartesian products of graphs." Discussiones Mathematicae Graph Theory 27.1 (2007): 175-178. <http://eudml.org/doc/270655>.

@article{XinminHou2007,

abstract = {Let γₜ(G) and $γ_\{pr\}(G)$ denote the total domination and the paired domination numbers of graph G, respectively, and let G □ H denote the Cartesian product of graphs G and H. In this paper, we show that γₜ(G)γₜ(H) ≤ 5γₜ(G □ H), which improves the known result γₜ(G)γₜ(H) ≤ 6γₜ(G □ H) given by Henning and Rall.},

author = {Xinmin Hou},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {total domination number; Cartesian product; Vizing's conjecture; domination numbers},

language = {eng},

number = {1},

pages = {175-178},

title = {Total domination of Cartesian products of graphs},

url = {http://eudml.org/doc/270655},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Xinmin Hou

TI - Total domination of Cartesian products of graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2007

VL - 27

IS - 1

SP - 175

EP - 178

AB - Let γₜ(G) and $γ_{pr}(G)$ denote the total domination and the paired domination numbers of graph G, respectively, and let G □ H denote the Cartesian product of graphs G and H. In this paper, we show that γₜ(G)γₜ(H) ≤ 5γₜ(G □ H), which improves the known result γₜ(G)γₜ(H) ≤ 6γₜ(G □ H) given by Henning and Rall.

LA - eng

KW - total domination number; Cartesian product; Vizing's conjecture; domination numbers

UR - http://eudml.org/doc/270655

ER -

## References

top- [1] E.J. Cockayne, R.M. Dawes and S.T. Hedetniemi, Total domination in graphs, Networks 10 (1980) 211-219, doi: 10.1002/net.3230100304. Zbl0447.05039
- [2] W.E. Clark and S. Suen, An inequality related to Vizing's conjecture, Electron. J. Combin. 7 (2000), No.1, Note 4, 3pp. (electronic). Zbl0947.05056
- [3] M.A. Henning and D.F. Rall, On the total domination number of Cartesian products of graphs, Graphs and Combinatorics 21 (2005) 63-69, doi: 10.1007/s00373-004-0586-8. Zbl1062.05109
- [4] T.W. Haynes and P.J. Slater, Paired-domination in graphs, Networks 32 (1998) 199-206, doi: 10.1002/(SICI)1097-0037(199810)32:3<199::AID-NET4>3.0.CO;2-F Zbl0997.05074
- [5] V.G. Vizing, Some unsolved problems in graph theory, Usp. Mat. Nauk 23 (1968), no. 6(144) 117-134. Zbl0177.52301

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