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Geodetic rays and fibers in periodic graphs

Research output: Journal contributions › Journal articles › Research › peer-review

Standard

Geodetic rays and fibers in periodic graphs. / Niemeyer, Peter; Watkins, Mark E.
In: Journal of Graph Theory, Vol. 34, No. 1, 05.2000, p. 67-88.

Research output: Journal contributions › Journal articles › Research › peer-review

Harvard

Niemeyer, P & Watkins, ME 2000, 'Geodetic rays and fibers in periodic graphs', Journal of Graph Theory, vol. 34, no. 1, pp. 67-88. https://doi.org/10.1002/(SICI)1097-0118(200005)34:1<67::AID-JGT7>3.0.CO;2-V

APA

Niemeyer, P., & Watkins, M. E. (2000). Geodetic rays and fibers in periodic graphs. Journal of Graph Theory, 34(1), 67-88. https://doi.org/10.1002/(SICI)1097-0118(200005)34:1<67::AID-JGT7>3.0.CO;2-V

Vancouver

Niemeyer P, Watkins ME. Geodetic rays and fibers in periodic graphs. Journal of Graph Theory. 2000 May;34(1):67-88. doi: 10.1002/(SICI)1097-0118(200005)34:1<67::AID-JGT7>3.0.CO;2-V

Bibtex

@article{ad6eee18a3094a1ebf2217fe8cf15223,
title = "Geodetic rays and fibers in periodic graphs",
abstract = "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.",
keywords = "Business informatics, locally finite, almost transitive, fiber, geodesic, periodic graph, translatable",
author = "Peter Niemeyer and Watkins, {Mark E.}",
year = "2000",
month = may,
doi = "10.1002/(SICI)1097-0118(200005)34:1<67::AID-JGT7>3.0.CO;2-V",
language = "English",
volume = "34",
pages = "67--88",
journal = "Journal of Graph Theory",
issn = "0364-9024",
publisher = "John Wiley & Sons Inc.",
number = "1",

}

RIS

TY - JOUR

T1 - Geodetic rays and fibers in periodic graphs

AU - Niemeyer, Peter

AU - Watkins, Mark E.

PY - 2000/5

Y1 - 2000/5

N2 - 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.

AB - 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.

KW - Business informatics

KW - locally finite

KW - almost transitive

KW - fiber

KW - geodesic

KW - periodic graph

KW - translatable

UR - http://www.scopus.com/inward/record.url?scp=0034180090&partnerID=8YFLogxK

U2 - 10.1002/(SICI)1097-0118(200005)34:1<67::AID-JGT7>3.0.CO;2-V

DO - 10.1002/(SICI)1097-0118(200005)34:1<67::AID-JGT7>3.0.CO;2-V

M3 - Journal articles

VL - 34

SP - 67

EP - 88

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 1

ER -

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Research output: Books and anthologies › Conference proceedings › Research

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Research output: Contributions to collected editions/works › Article in conference proceedings › Research › peer-review

DOI