We prove that the smallest cardinality of a maximal packing in any tree is at most the cardinality of an R-annihilated set. As a corollary to this result we point out that a set of parameters of trees involving packing, perfect neighbourhood, R-annihilated, irredundant and dominating sets is totally ordered. The class of trees for which all these parameters are equal is described and we give an example of a tree in which most of them are distinct.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1069,
author = {E.J. Cockayne and O. Favaron and J. Puech and C.M. Mynhardt},
title = {An inequality chain of domination parameters for trees},
journal = {Discussiones Mathematicae Graph Theory},
volume = {18},
year = {1998},
pages = {127-142},
zbl = {0914.05058},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1069}
}
E.J. Cockayne; O. Favaron; J. Puech; C.M. Mynhardt. An inequality chain of domination parameters for trees. Discussiones Mathematicae Graph Theory, Tome 18 (1998) pp. 127-142. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1069/
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