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COMBINATORICS
2006

Edge-Magic Group Labellings of Countable Graphs

8 years 11 months ago
Edge-Magic Group Labellings of Countable Graphs
We investigate the existence of edge-magic labellings of countably infinite graphs by abelian groups. We show for that for a large class of abelian groups, including the integers Z, there is such a labelling whenever the graph has an infinite set of disjoint edges. A graph without an infinite set of disjoint edges must be some subgraph of H + I, where H is some finite graph and I is a countable set of isolated vertices. Using power series of rational functions, we show that any edge-magic Z-labelling of H + I has almost all vertex labels making up pairs of half-modulus classes. We also classify all possible edge-magic Z-labellings of H +I under the assumption that the vertices of the finite graph are labelled consecutively.
Nicholas J. Cavenagh, Diana Combe, Adrian M. Nelso
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where COMBINATORICS
Authors Nicholas J. Cavenagh, Diana Combe, Adrian M. Nelson
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