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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; $Y$-dominating function of a graph; $Y$-domination number of a graph
Summary:
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.
References:
[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. MR 1405819 | Zbl 0842.05051
[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. MR 1041627 | Zbl 0691.05043
[4] Bange D. W., Barkauskas A. E.: Host L. H., Slater P. J.: Generalized domination and efficient domination in graphs. Discrete Math. 159 (1996), 1-11. DOI 10.1016/0012-365X(95)00094-D | MR 1415278
[5] Zelinka B.: On k-ply domatic numbers of graphs. Math. Slovaca 34 (1984), 313-318. MR 0756989 | Zbl 0602.05039
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