TOTAL DOMINATIONS IN P6-FREE GRAPHS

Title & Authors
TOTAL DOMINATIONS IN P6-FREE GRAPHS
Chen, Xue-Gang; Sohn, Moo Young;

Abstract
In this paper, we prove that the total domination number of a $\small{P_6}$-free graph of order $\small{n{\geq}3}$ and minimum degree at least one which is not the cycle of length 6 is at most $\small{\frac{n+1}{2}}$, and the bound is sharp.
Keywords
total domination numbers;$\small{P_6}$-free graphs;
Language
English
Cited by
References
1.
D. Archdeacon, J. Ellis-monagham, D. Fisher, D. Froncek, P. C. B. Lam, S. Seager, B. Wei, and R. Yuster, Some remarks on domination, J. Graph Theory 46 (2004), no. 3, 207-210.

2.
R. C. Brigham, J. R. Carrington, and R. P. Vitray, Connected graphs with maximum total domination number, J. Combin. Math. Combin. Comput. 34 (2000), 81-95.

3.
E. J. Cockayne, R. M. Dawes, and S. T. Hedetniemi, Total domination in graphs, Networks 10 (1980), no. 3, 211-219.

4.
P. Dorbec and S. Gravier, Paired-domination in $P_5$-free graphs, Graphs Combin. 24 (2008), no. 4, 303-308.

5.
O. Favaron and M. A. Henning, Total domination in claw-free graphs with minimum degree 2, Discrete Math. 308 (2008), no. 15, 3213-3219.

6.
O. Favaron, M. A. Henning, C. M. Mynhart, and J. Puech, Total domination in graphs with minimum degree three, J. Graph Theory 34 (2000), no. 1, 9-19.

7.
M. A. Henning, Graphs with large total domination number, J. Graph Theory 35 (2000), no. 1, 21-45.