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

Maya Mohsin Ahmed

doi:10.1007/s00026-008-0349-y

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

Maya Mohsin Ahmed

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	241-269
Number of pages	29
Journal	Annals of Combinatorics
Volume	12
Issue number	3
DOIs	https://doi.org/10.1007/s00026-008-0349-y
Publication status	Published - 01-10-2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

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10.1007/s00026-008-0349-y

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

Abstract

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