Polytopes of magic labelings of graphs and the faces of the birkhoff polytope

Maya Mohsin Ahmed

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1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)241-269
Number of pages29
JournalAnnals of Combinatorics
Issue number3
Publication statusPublished - 01-10-2008
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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