Total domination of Cartesian products of graphs

• Autorzy: Xinmin Hou
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

total domination number; Cartesian product; Vizing's conjecture

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2007
• Tom: 27
• Numer: 1
• Strony: 175-178

Daty

wydano

2007

otrzymano

2006-03-07

poprawiono

2006-10-25

Twórcy

autor

Xinmin Hou

• Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, China

Bibliografia

• [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.
• [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).
• [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.
• [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
• [5] V.G. Vizing, Some unsolved problems in graph theory, Usp. Mat. Nauk 23 (1968), no. 6(144) 117-134.

Identyfikatory

DOI

10.7151/dmgt.1353