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Jacobian Tori Associated with a Finite Graph and Its Abelian Covering Graphs

✍ Scribed by Motoko Kotani; Toshikazu Sunada

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 176 KB
Volume: 24
Category: Article
ISSN: 0196-8858
DOI: 10.1006/aama.1999.0672

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✦ Synopsis

We develop a graph-theoretic analogue of the Jacobian torus, which is defined, for a finite graph X, as the torus H 1 X R /H 1 X Z with a natural flat metric. It is observed that this notion, especially the volume of Jacobian tori, appears in many contexts of graph theory.