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Discussiones Mathematicae Graph Theory  18(1) (1998)   127-142
DOI: https://doi.org/10.7151/dmgt.1069

AN INEQUALITY CHAIN OF DOMINATION PARAMETERS FOR TREES

E.J. Cockayne Department of Mathematics, University of Victoria Victoria, British Columbia, Canada V8W 3P4 e-mail: cockayne@smart.math.uvic.ca

O. Favaron and J. Puech LRI, Bât. 490, Université de Paris-Sud Orsay, France 91405 e-mail: of@lri.fre-mail: puech@lri.fr

C.M. Mynhardt Department of Mathematics, University of South Africa PO Box 392, 0003 Pretoria, South Africa e-mail: mynhacm@alpha.unisa.ac.za

Abstract

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.

Keywords: domination, irredundance, packing, perfect neighbourhoods, annihilation.

1991 Mathematics Subject Classification: 05C70, 05C05.

References

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Received 30 October 1997