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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.

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