Abstract.
In this article, we construct and enumerate magic labelings of graphs using Hilbert bases of polyhedral cones and Ehrhart quasi-polynomials of polytopes. This enables us to generate and enumerate perfect matchings of a graph via magic labelings of the graph. We explore the correspondence of magic labelings of graphs with magic squares and define polytopes of magic labelings to give a description of the faces of the Birkhoff polytope as polytopes of magic labelings of digraphs.
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Received September 9, 2004
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Ahmed, M.M. Polytopes of Magic Labelings of Graphs and the Faces of the Birkhoff Polytope. Ann. Comb. 12, 241–269 (2008). https://doi.org/10.1007/s00026-008-0349-y
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DOI: https://doi.org/10.1007/s00026-008-0349-y
Keywords:
- symmetric magic squares
- magic labelings of graphs
- Polyhedral cones
- Polytopes
- Hilbert basis
- Ehrhart quasi-polynomials
- Invariant rings
- Birkhoff polytope