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On zero-sum magic graphs and their null sets
by Ebrahim Salehi

Vol. 3 No. 2 (2008) P.255~P.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.

KEYWORDS
magic, non-magic, zero-sum, null set, uniformly null

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 05C78

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