Fractional global domination in graphs

Subramanian Arumugam; Kalimuthu Karuppasamy; Ismail Sahul Hamid

Subramanian Arumugam ; Kalimuthu Karuppasamy ; Ismail Sahul Hamid

Discussiones Mathematicae Graph Theory, Tome 30 (2010), p. 33-44 / Harvested from The Polish Digital Mathematics Library

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Résumé

Let G = (V,E) be a graph. A function g:V → [0,1] is called a global dominating function (GDF) of G, if for every v ∈ V, $g (N [v]) = \sum_{u \in N [v]} g (u) \geq 1$ and $g (\bar{N (v)}) = \sum_{u \notin N (v)} g (u) \geq 1$ . A GDF g of a graph G is called minimal (MGDF) if for all functions f:V → [0,1] such that f ≤ g and f(v) ≠ g(v) for at least one v ∈ V, f is not a GDF. The fractional global domination number $γ_{f g} (G)$ is defined as follows: $γ_{f g} (G)$ = min|g|:g is an MGDF of G where $| g | = \sum_{v \in V} g (v)$ . In this paper we initiate a study of this parameter.

Publié le : 2010-01-01

Zbl 1214.05100

EUDML-ID : urn:eudml:doc:270977

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     title = {Fractional global domination in graphs},
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     zbl = {1214.05100},
     language = {en},
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Subramanian Arumugam; Kalimuthu Karuppasamy; Ismail Sahul Hamid. Fractional global domination in graphs. Discussiones Mathematicae Graph Theory, Tome 30 (2010) pp. 33-44. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1474/

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