DMGT

Discussiones Mathematicae Graph Theory 24(2) (2004) 165-169
DOI: https://doi.org/10.7151/dmgt.1222

LOWER BOUND ON THE DOMINATION NUMBER OF A TREE

Magdalena Lemańska

Department of Mathematics
Gdańsk University of Technology
Narutowicza 11/12, 80-952 Gdańsk, Poland
e-mail: magda@mif.pg.gda.pl Abstract We prove that the domination number γ(T) of a tree T on n ≥ 3 vertices and with n₁ endvertices satisfies inequality γ(T) ≥ [(n+2−n₁)/3] and we characterize the extremal graphs.

Keywords: domination number, tree.

2000 Mathematics Subject Classification: 05C05, 05C69.

References

[1]	O. Favaron, A bound on the independent domination number of a tree, Vishwa International Journal of Graph Theory 1 (1992) 19-27.
[2]	J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan. London, 1976).

Received 24 September 2001
Revised 10 December 2003