DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2019: 0.755

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory  17(1) (1997)   147-153
DOI: 10.7151/dmgt.1048

GENERALIZED DOMINATION, INDEPENDENCE AND IRREDUDANCE IN GRAPHS

Mieczysław Borowiecki
Danuta Michalak
Elżbieta Sidorowicz

Institute of Mathematics, Technical University of Zielona Góra
Podgórna 50, 65-246 Zielona Góra, Poland

 e-mail:

m.borowiecki@im.uz.zgora.pl

d.michalak@im.uz.zgora.pl

e.sidorowicz@im.uz.zgora.pl

Abstract

The purpose of this paper is to present some basic properties of  P-dominating, P-independent, and P-irredundant sets in graphs which generalize well-known properties of dominating, independent and irredundant sets, respectively.

Keywords: hereditary property of graphs, generalized domination, independence and irredundance numbers.

1991 Mathematics Subject Classification: 05C35.

References

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[2] E.J. Cockayne and S.T. Hedetniemi, Independence graphs, in: Proc. 5th Southeast Conf. Combinatorics, Graph Theory and Computing, Utilitas Mathematica (Winnepeg, 1974) 471-491.
[3] E.J. Cockayne, S.T. Hedetniemi and D.J. Miller, Properties of hereditary hypergraphs and middle graphs, Canad. Math. Bull. 21 (1978) 461-468, doi: 10.4153/CMB-1978-079-5.
[4] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completness (W.H. Freeman, San Francisco, CA, 1979).
[5] M.A. Henning and H.C. Swart, Bounds on a generalized domination parameter, Quaestiones Math. 13 (1990) 237-253, doi: 10.1080/16073606.1990.9631615.
[6] O. Ore, Theory of Graphs (Amer. Math. Soc. Colloq. Publ. 38, Providence, R. I., 1962).