05194469

j

05194469 Salehi, Ebrahim Zero-sum magic graphs and their null sets. Ars Comb. 82, 41-53 (2007). 2007 Charles Babbage Research Centre, Winnipeg, MB EN magic non-magic zero-sum null set egde labeling vertex labeling zero sum h-magic graph Summary: For any $h\in \Bbb N$, a graph $G=(V,E)$ is said to be $h$-magic if there exists a labeling $l\:E(G)\to \Bbb Z_h-\{0\}$ such that the induced vertex labeling $l^+\:V(G)\to \Bbb Z_h$ 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 $h\in \Bbb N$ for which $G$ admits a zero-sum $h$-magic labeling. In this paper we will identify several classes of zero sum magic graphs and will determine their null sets.