DMGT

Discussiones Mathematicae Graph Theory 25(1-2) (2005) 7-12
DOI: https://doi.org/10.7151/dmgt.1254

ON DOMINATION IN GRAPHS

Frank Göring

Department of Mathematics
Chemnitz University of Technology
D-09107 Chemnitz, Germany
e-mail: frank.goering@mathematik.tu-chemnitz.de

Jochen Harant

Department of Mathematics
Technical University of Ilmenau
D-98684 Ilmenau, Germany
e-mail: harant@mathematik.tu-ilmenau.de

Abstract

For a finite undirected graph G on n vertices two continuous optimization problems taken over the n-dimensional cube are presented and it is proved that their optimum values equal the domination number γ of G. An efficient approximation method is developed and known upper bounds on γ are slightly improved.

Keywords: graph, domination.

2000 Mathematics Subject Classification: 05C69.

References

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[3]	R. Diestel, Graph Theory, Graduate Texts in Mathematics (Springer, 1997).
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[6]	J. Harant, Some news about the independence number of a graph, Discuss. Math. Graph Theory 20 (2000) 71-79, doi: 10.7151/dmgt.1107.
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Received 23 September 2003
Revised 15 June 2004