Geodetic rays and fibers in periodic graphs

Publikation: Beiträge in ZeitschriftenZeitschriftenaufsätzeForschungbegutachtet

Standard

Geodetic rays and fibers in periodic graphs. / Niemeyer, Peter; Watkins, Mark E.
in: Journal of Graph Theory, Jahrgang 34, Nr. 1, 05.2000, S. 67-88.

Publikation: Beiträge in ZeitschriftenZeitschriftenaufsätzeForschungbegutachtet

Harvard

APA

Vancouver

Niemeyer P, Watkins ME. Geodetic rays and fibers in periodic graphs. Journal of Graph Theory. 2000 Mai;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 = "Wiley-Liss 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 -

Zuletzt angesehen

Aktivitäten

  1. Sustainability and internal supply chain management – A conceptual approach to intra-organisational knowledge transfer
  2. Hermann von Helmholtz-Zentrum für Kulturtechnik (Externe Organisation)
  3. Analyse des Feedbacks von (angehenden) Lehrkräften mit Microteaching Videos.
  4. What's it good for? : Functions of arts and culture for Hamburg's urban development
  5. Alumni Association - UC Berkeley (Externe Organisation)
  6. Das ,gute Leben‘: Was heißt das für andere?
  7. Initiativgruppe zur Erweiterung von Lernmöglichkeiten - IGEL 2011
  8. Education for Sustainability: "Going Green" - A Project in Progess
  9. Division of Occupational Psychology Annual Conference - DOP 2013
  10. Lively Artifacts. BCL-Engineers and their Self-Organizing Machines (The 26th Annual Meeting of the Society for Literature, Science and the Arts [SLSA])
  11. Time rebounds, time wealth, and sustainability: A conceptual model to empirically analyze the significance of time use for sustainable consumption
  12. Contentious politics and the role of connective technologies in Russian anti-war networks
  13. Inaugural Meeting of the Earth System Governance Taskforce on Knowledge Cumulation at Earth System Governance Taskforce and Meeting Day - 2021
  14. Sprachbildendes Engagement durch Partizipation in der Lehrer:innenbildung: Implementation von Service Learning durch das Projekt LehrWEP
  15. Arbeitsgruppe GeschlechterGesellschaftsTheorien (Externe Organisation)
  16. „Das ewig Dauernde in uns“. Immanenz und Transzendenz in Stifters Nachsommer
  17. 4th Keep it Simple Make it Fast! - KISMIF 2018
  18. The German Assisted Return Regime – an interpretive approach
  19. Lost in reflection – Zur Möglichkeit von Bildung im Kontext von Distance Learning“.