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Magic labellings of graphs over finite abelian groups. (English) Zbl 1050.05107
The notions of vertex-magic graphs, edge-magic graphs, and totally magic graphs have been well studied. A graph \((V,E)\) is vertex-magic (edge-magic), when we can assign each vertex and edge a different number from \(\{1,2, \dots, | V| +| E| \}\) such that all vertices (all edges) have the same sum of its weight and the weights of its incident edges (vertices). When a graph is both vertex-magic and edge-magic, it is totally magic. In this paper, the notion is generalized to the case that we do not use integers but the elements of an abelian group of order \(| V| +| E| \) for labeling the vertices and edges. Such magic labelings of star graphs are then investigated.

05C78 Graph labelling (graceful graphs, bandwidth, etc.)
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)