Generalized domination, independence and irredudance in graphs

Mieczysław Borowiecki; Danuta Michalak; Elżbieta Sidorowicz

Discussiones Mathematicae Graph Theory (1997)

  • Volume: 17, Issue: 1, page 147-153
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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Mieczysław Borowiecki, Danuta Michalak, and Elżbieta Sidorowicz. "Generalized domination, independence and irredudance in graphs." Discussiones Mathematicae Graph Theory 17.1 (1997): 147-153. <http://eudml.org/doc/270465>.

@article{MieczysławBorowiecki1997,
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.},
author = {Mieczysław Borowiecki, Danuta Michalak, Elżbieta Sidorowicz},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {hereditary property of graphs; generalized domination; independence and irredundance numbers; hereditary graph properties; domination},
language = {eng},
number = {1},
pages = {147-153},
title = {Generalized domination, independence and irredudance in graphs},
url = {http://eudml.org/doc/270465},
volume = {17},
year = {1997},
}

TY - JOUR
AU - Mieczysław Borowiecki
AU - Danuta Michalak
AU - Elżbieta Sidorowicz
TI - Generalized domination, independence and irredudance in graphs
JO - Discussiones Mathematicae Graph Theory
PY - 1997
VL - 17
IS - 1
SP - 147
EP - 153
AB - 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.
LA - eng
KW - hereditary property of graphs; generalized domination; independence and irredundance numbers; hereditary graph properties; domination
UR - http://eudml.org/doc/270465
ER -

References

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  1. [1] M. Borowiecki and P. Mihók, Hereditary Properties of Graphs, in: Advances in Graph Theory (Vishwa Inter. Publications, 1991) 41-68. 
  2. [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. Zbl0305.05114
  3. [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. Zbl0393.05044
  4. [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). Zbl0411.68039
  5. [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. Zbl0709.05029
  6. [6] O. Ore, Theory of Graphs (Amer. Math. Soc. Colloq. Publ. 38, Providence, R. I., 1962). 

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