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

Maya Mohsin Ahmed

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)241-269
Number of pages29
JournalAnnals of Combinatorics
Volume12
Issue number3
DOIs
Publication statusPublished - 01-10-2008
Externally publishedYes

Fingerprint

Polytopes
Polytope
Labeling
Face
Graph in graph theory
Hilbert Basis
Polyhedral Cones
Magic square
Perfect Matching
Digraph
Correspondence
Polynomial

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

Cite this

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Polytopes of magic labelings of graphs and the faces of the birkhoff polytope. / Ahmed, Maya Mohsin.

In: Annals of Combinatorics, Vol. 12, No. 3, 01.10.2008, p. 241-269.

Research output: Contribution to journalArticle

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