Geodesic
A lower bound for the irredundance number of trees
Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 2, pp. 209-215.

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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
Keywords: irredundance, tree, domination 
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Poschen, Michael; Volkmann, Lutz. A lower bound for the irredundance number of trees. Discussiones Mathematicae. Graph Theory, Tome 26 (2006) no. 2, pp. 209-215. http://geodesic.mathdoc.fr/item/DMGT_2006_26_2_a2/

[1] E.J. Cockayne, Irredundance, secure domination, and maximum degree in trees, unpublished manuscript (2004).

[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.

[3] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, Inc., New York, 1998).

[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.