On the uniqueness of D-vertex magic constant

Title: On the uniqueness of D-vertex magic constant
Creator: Arumugam, S.; Kamatchi, N.; Vijayakumar, G. R.
Relation: Discussiones Mathematicae: Graph Theory Vol. 34, Issue 2, p. 279-286
Publisher Link: http://dx.doi.org/10.7151/dmgt.1728
Publisher: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Gora
Resource Type: journal article
Date: 2014
Description: Let G = (V,E) be a graph of order n and let D ⊆ {0, 1, 2, 3, . . .}. For v ∈ V, let N_D(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, Σ_u∈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.
Subject: distance magic graph; D-vertex magic graph; magic constant; dominating function; fractional domination number
Identifier: http://hdl.handle.net/1959.13/1303640
Identifier: uon:20696
Identifier: ISSN:1234-3099
Language: eng
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