- 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 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, Σu∈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
- Reviewed
- Hits: 1999
- Visitors: 1976
- Downloads: 0
Thumbnail | File | Description | Size | Format |
---|