On the uniqueness of d-vertex magic constant
S. Arumugam ; N. Kamatchi ; G.R. Vijayakumar
Discussiones Mathematicae Graph Theory, Tome 34 (2014), p. 279-286 / Harvested from The Polish Digital Mathematics Library
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Let G = (V,E) be a graph of order n and let D ⊆ {0, 1, 2, 3, . . .}. For v ∈ V, let ND(v) = {u ∈ V : d(u, v) ∈ D}. The graph G is said to be D-vertex magic if there exists a bijection f : V (G) → {1, 2, . . . , n} such that for all v ∈ V, ∑uv∈ND(v) f(u) is a constant, called D-vertex magic constant. O’Neal and Slater have proved the uniqueness of the D-vertex magic constant by showing that it can be determined by the D-neighborhood fractional domination number of the graph. In this paper we give a simple and elegant proof of this result. Using this result, we investigate the existence of distance magic labelings of complete r-partite graphs where r ≥ 4.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:267976 
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S. Arumugam; N. Kamatchi; G.R. Vijayakumar. On the uniqueness of d-vertex magic constant. Discussiones Mathematicae Graph Theory, Tome 34 (2014) pp. 279-286. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1728/

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