Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: fractional domination numbe

Sortuj według:

Ogranicz wyniki do:

On the uniqueness of d-vertex magic constant

100%

Arumugam S., Kamatchi N., Vijayakumar G. R.

Discussiones Mathematicae Graph Theory

2014

tom 34

nr 2

279-286

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.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Arumugam S.

1 Kamatchi N.

1 Vijayakumar G. R.

1 2014

Wyniki wyszukiwania

On the uniqueness of d-vertex magic constant