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  18(1) (1998)   63-72
DOI: 10.7151/dmgt.1063

PAIRED-DOMINATION

S. Fitzpatrick

Dalhousie University, Halifax, Canada, B3H 3J5

and

B. Hartnell

Saint Mary's University, Halifax, Canada, B3H 3C3

Abstract

We are interested in dominating sets (of vertices) with the additional property that the vertices in the dominating set can be paired or matched via existing edges in the graph. This could model the situation of guards or police where each has a partner or backup. This paper will focus on those graphs in which the number of matched pairs of a minimum dominating set of this type equals the size of some maximal matching in the graph. In particular, we characterize the leafless graphs of girth seven or more of this type.

Keywords: domination, paired-domination, matching.

1991 Mathematics Subject Classification: 05C75.

References

[1] T.W. Haynes and P.J. Slater, Paired-domination in graphs, submitted for publication.
[2] T.W. Haynes and P.J. Slater, Paired-domination and the paired-domatic number, Congressus Numerantium 109 (1995) 65-72.

Received 18 February 1997
Revised 12 September 1997