ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 30(4) (2010) 563-574
DOI: 10.7151/dmgt.1514


Michael A. Henning

Department of Mathematics
University of Johannesburg
Auckland Park, 2006 South Africa

Christian Löwenstein and Dieter Rautenbach

Institut für Mathematik
TU Ilmenau, Postfach 100565
D-98684 Ilmenau, Germany
e-mails: {christian.loewenstein, dieter.rautenbach}


A recent result of Henning and Southey (A note on graphs with disjoint dominating and total dominating set, Ars Comb. 89 (2008), 159-162) implies that every connected graph of minimum degree at least three has a dominating set D and a total dominating set T which are disjoint. We show that the Petersen graph is the only such graph for which D∪T necessarily contains all vertices of the graph.

Keywords: domination, total domination, domatic number, vertex partition, Petersen graph.

2010 Mathematics Subject Classification: 05C69.


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Received 18 July 2009
Revised 9 November 2009
Accepted 9 November 2009