- Tytuł:
- On the uniqueness of $D$-vertex magic constant
- Autorzy:
-
Arumugam, S.
Kamatchi, N.
Vijayakumar, G.R. - Powiązania:
- https://bibliotekanauki.pl/articles/30148233.pdf
- Data publikacji:
- 2014-05-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
distance magic graph
D-vertex magic graph
magic constant
dominating function
fractional domination number - Opis:
- 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 $v ∈ V, _{∑uv∈ND(v)} f(u)$ 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 $r ≥ 4$.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2014, 34, 2; 279-286
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł