Dominating functions of graphs with two values

Bohdan Zelinka

Mathematica Bohemica (1998)

  • Volume: 123, Issue: 3, page 263-270
  • ISSN: 0862-7959

Abstract

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The Y -domination number of a graph for a given number set Y was introduced by D. W. Bange, A. E. Barkauskas, L. H. Host and P. J. Slater as a generalization of the domination number of a graph. It is defined using the concept of a Y -dominating function. In this paper the particular case where Y = { 0 , 1 / k } for a positive integer k is studied.

How to cite

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Zelinka, Bohdan. "Dominating functions of graphs with two values." Mathematica Bohemica 123.3 (1998): 263-270. <http://eudml.org/doc/248313>.

@article{Zelinka1998,
abstract = {The $Y$-domination number of a graph for a given number set $Y$ was introduced by D. W. Bange, A. E. Barkauskas, L. H. Host and P. J. Slater as a generalization of the domination number of a graph. It is defined using the concept of a $Y$-dominating function. In this paper the particular case where $Y = \lbrace 0,1/k\rbrace $ for a positive integer $k$ is studied.},
author = {Zelinka, Bohdan},
journal = {Mathematica Bohemica},
keywords = {generalization of domination number of a graph; $Y$-dominating function of a graph; $Y$-domination number of a graph; generalization of domination number of a graph},
language = {eng},
number = {3},
pages = {263-270},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Dominating functions of graphs with two values},
url = {http://eudml.org/doc/248313},
volume = {123},
year = {1998},
}

TY - JOUR
AU - Zelinka, Bohdan
TI - Dominating functions of graphs with two values
JO - Mathematica Bohemica
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 123
IS - 3
SP - 263
EP - 270
AB - The $Y$-domination number of a graph for a given number set $Y$ was introduced by D. W. Bange, A. E. Barkauskas, L. H. Host and P. J. Slater as a generalization of the domination number of a graph. It is defined using the concept of a $Y$-dominating function. In this paper the particular case where $Y = \lbrace 0,1/k\rbrace $ for a positive integer $k$ is studied.
LA - eng
KW - generalization of domination number of a graph; $Y$-dominating function of a graph; $Y$-domination number of a graph; generalization of domination number of a graph
UR - http://eudml.org/doc/248313
ER -

References

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  1. Dunbar J., Hedetniemi S. T., Henning M. A., Slater P. J., Signed domination in graphs, In: Graph Theory, Combinatorics and Applications (ed. Y. Alavi, A. Schwenk). Wiley, New York, 1995, pp. 311-321. (1995) Zbl0842.05051MR1405819
  2. Dunbar J., Hedetniemi S. T.: Henning M. A., McRae A., Minus domination in graphs, Computers Math. Appl. To appear. 
  3. Grinstead D. L., Slater P. J., Fractional domination and fractional packing in graphs, Congr. Numer. 71 (1990), 153-172. (1990) Zbl0691.05043MR1041627
  4. Bange D. W., Barkauskas A. E.: Host L. H., Slater P. J., 10.1016/0012-365X(95)00094-D, Discrete Math. 159 (1996), 1-11. (1996) MR1415278DOI10.1016/0012-365X(95)00094-D
  5. Zelinka B., On k-ply domatic numbers of graphs, Math. Slovaca 34 (1984), 313-318. (1984) Zbl0602.05039MR0756989

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