# A lower bound for the irredundance number of trees

• Volume: 26, Issue: 2, page 209-215
• ISSN: 2083-5892

top

## Abstract

top
Let ir(G) and γ(G) be the irredundance number and domination number of a graph G, respectively. The number of vertices and leaves of a graph G are denoted by n(G) and n₁(G). If T is a tree, then Lemańska [4] presented in 2004 the sharp lower bound γ(T) ≥ (n(T) + 2 - n₁(T))/3. In this paper we prove ir(T) ≥ (n(T) + 2 - n₁(T))/3. for an arbitrary tree T. Since γ(T) ≥ ir(T) is always valid, this inequality is an extension and improvement of Lemańska's result.

## How to cite

top

Michael Poschen, and Lutz Volkmann. "A lower bound for the irredundance number of trees." Discussiones Mathematicae Graph Theory 26.2 (2006): 209-215. <http://eudml.org/doc/270471>.

@article{MichaelPoschen2006,
abstract = { Let ir(G) and γ(G) be the irredundance number and domination number of a graph G, respectively. The number of vertices and leaves of a graph G are denoted by n(G) and n₁(G). If T is a tree, then Lemańska [4] presented in 2004 the sharp lower bound γ(T) ≥ (n(T) + 2 - n₁(T))/3. In this paper we prove ir(T) ≥ (n(T) + 2 - n₁(T))/3. for an arbitrary tree T. Since γ(T) ≥ ir(T) is always valid, this inequality is an extension and improvement of Lemańska's result. },
author = {Michael Poschen, Lutz Volkmann},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {irredundance; tree; domination},
language = {eng},
number = {2},
pages = {209-215},
title = {A lower bound for the irredundance number of trees},
url = {http://eudml.org/doc/270471},
volume = {26},
year = {2006},
}

TY - JOUR
AU - Michael Poschen
AU - Lutz Volkmann
TI - A lower bound for the irredundance number of trees
JO - Discussiones Mathematicae Graph Theory
PY - 2006
VL - 26
IS - 2
SP - 209
EP - 215
AB - Let ir(G) and γ(G) be the irredundance number and domination number of a graph G, respectively. The number of vertices and leaves of a graph G are denoted by n(G) and n₁(G). If T is a tree, then Lemańska [4] presented in 2004 the sharp lower bound γ(T) ≥ (n(T) + 2 - n₁(T))/3. In this paper we prove ir(T) ≥ (n(T) + 2 - n₁(T))/3. for an arbitrary tree T. Since γ(T) ≥ ir(T) is always valid, this inequality is an extension and improvement of Lemańska's result.
LA - eng
KW - irredundance; tree; domination
UR - http://eudml.org/doc/270471
ER -

## References

top
1. [1] E.J. Cockayne, Irredundance, secure domination, and maximum degree in trees, unpublished manuscript (2004). Zbl1233.05143
2. [2] E.J. Cockayne, P.H.P. Grobler, S.T. Hedetniemi and A.A. McRae, What makes an irredundant set maximal? J. Combin. Math. Combin. Comput. 25 (1997) 213-224. Zbl0907.05032
3. [3] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, Inc., New York, 1998). Zbl0890.05002
4. [4] M. Lemańska, Lower bound on the domination number of a tree, Discuss. Math. Graph Theory 24 (2004) 165-169, doi: 10.7151/dmgt.1222. Zbl1063.05035

## NotesEmbed?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.