2008 / June Volume 3 No.2
On zero-sum magic graphs and their null sets
| Published Date |
2008 / June
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|---|---|
| Title | On zero-sum magic graphs and their null sets |
| Author | |
| Keyword | |
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| Pagination | 255-264 |
| Abstract | For any $h \in N$, a graph $G = (V,E)$ is said to be $h$-magic if there exists a labeling $l : E(G) \to \mathbb{Z}_h $ - {0} such that the induced vertex labeling $l^+ : V(G) \to \mathbb{Z}_h$ defined by
$l^+(v) = \sum_{uv\in E(G)} l(uv)$ is a constant map. When this constant is 0 we call $G$ a zero-sum $h$-magic graph. The null set of $G$ is the set of all natural numbers $h \in \mathbb{N}$ for which $G$ admits a zero-sum $h$-magic labeling. A graph $G$ is said to be uniformly null if every magic labeling of $G$ induces zero sum. In this paper we will identify the null sets of the generalized theta graphs and introduce a class of uniformly null magic graphs. |
| AMS Subject Classification |
05C78
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| Received |
2007-07-14
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