DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 22(2) (2002) 233-246
DOI: 10.7151/dmgt.1172

TREES WITH UNIQUE MINIMUM TOTAL DOMINATING SETS

Teresa W. Haynes

Department of Mathematics
East Tennessee State University
Johnson City, TN 37614 USA

Michael A. Henning

Department of Mathematics
University of Natal
Private Bag X01
Pietermaritzburg, 3209 South Africa

Abstract

A set S of vertices of a graph G is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. We provide three equivalent conditions for a tree to have a unique minimum total dominating set and give a constructive characterization of such trees.

Keywords: domination, total domination.

2000 Mathematics Subject Classification: 05C069.

References

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Received 10 February 2001
Revised 6 November 2001