Name
Abstract | ||
|---|---|---|
A graph G of order n is said to be Sigma' labeled if there exist a bijection f : V(G) -> [n] and a constant c such that for all v is an element of V(G), Sigma(u is an element of 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 subset of N, let N-D(v) = {u is an element of V(G) : d(u, v) is an element of 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 is an element of V(G), Sigma(u is an element of 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. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1137/110834421 | SIAM JOURNAL ON DISCRETE MATHEMATICS |
Keywords | DocType | Volume |
graph labeling,vertex magic,Sigma labeling,distance magic graphs,neighborhood sums | Journal | 27 |
Issue | ISSN | Citations |
2 | 0895-4801 | 3 |
PageRank | References | Authors |
1.25 | 4 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Allen O'Neal | 1 | 4 | 1.86 |
| Peter J. Slater | 2 | 593 | 132.02 |