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UNIQUENESS OF VERTEX MAGIC CONSTANTS.
- Source :
-
SIAM Journal on Discrete Mathematics . 2013, Vol. 27 Issue 2, p708-716. 9p. - Publication Year :
- 2013
-
Abstract
- A graph G of order n is said to be ∑' labeled if there exist a bijection f : V (G) → [n] and a constant c such that for all v ∈ V(G), ∑u∈N[v]f(u) = c. The uniqueness of the constant c has been an open question that was posed by Prof. Arumugam at the 2010 IWOGL Conference in Duluth. The question of the uniqueness of such a constant can be extended to arbitrary neighborhoods and to arbitrary sets of labels. For a set D ⊂ N, let ND(v) = {u ∈ V(G): d(u, v) ∈ D}, and let W be a multiset of real numbers. Graph G is said to be (D, W)-vertex magic if there exists a bijection g : V(G) → W such that for all v ∈ V(G), ∑u∈ND(v)g(u) is a constant, called the (D, W)-vertex magic constant. In this paper we prove that, even for these more general conditions, a (D, W)-vertex magic constant will be unique. Moreover, the constant can be determined using a generalization of the fractional domination number of the graph. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GRAPH theory
*BIJECTIONS
*DOMINATING set
*INJECTIVE functions
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 08954801
- Volume :
- 27
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 89041336
- Full Text :
- https://doi.org/10.1137/110834421