Geodetic rays and fibers in periodic graphs

Publikation: Beiträge in ZeitschriftenZeitschriftenaufsätzeForschungbegutachtet

Authors

Using the notion of fibers, where two rays belong to the same fiber if and only if they lie within bounded Hausdorff-distance of one another, we study how many fibers of a graph contain a geodetic ray and how many essentially distinct geodetic rays such "geodetic fibers" must contain. A complete answer is provided in the case of locally finite graphs that admit an almost transitive action by some infinite finitely generated, abelian group. Such graphs turn out to have either finitely many or uncountably many geodetic fibers. Furthermore, with finitely many possible exceptions, each of these fibers contains uncountably many geodetic rays.
OriginalspracheEnglisch
ZeitschriftJournal of Graph Theory
Jahrgang34
Ausgabenummer1
Seiten (von - bis)67-88
Anzahl der Seiten22
ISSN0364-9024
DOIs
PublikationsstatusErschienen - 05.2000

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