On Group-Magic Eulerian Graphs

Abstract

Let $A$ be an abelian group. We call a graph $G=(V,E)$ $A$-magic if there exists a labeling $f:E(G)\to A^{\ast }$ such that the induced vertex set labeling $f^{+}:V(G)\to A$, defined by $f^{+}(v)=\sum _{(u,v)\in E(G)}f(u,v)$, is a constant map. In this paper, we present some algebraic properties of $A$-magic graphs. Using them, various results are obtained for group-magic eulerian graphs.