1. //
  2. Start
  3. //
  4. Publications
  5. Understanding the properties of isospect...
  6. Output formats
  7. //

Understanding the properties of isospectral points and pairs in graphs: The concept of orthogonal relation.

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

Standard

Understanding the properties of isospectral points and pairs in graphs: The concept of orthogonal relation. / Rücker, Christoph; Rücker, Gerta.
In: Journal of Mathematical Chemistry, Vol. 9, No. 3, 09.1992, p. 207-238.

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

Harvard

Rücker, C & Rücker, G 1992, 'Understanding the properties of isospectral points and pairs in graphs: The concept of orthogonal relation.', Journal of Mathematical Chemistry, vol. 9, no. 3, pp. 207-238. https://doi.org/10.1007/BF01165148

APA

Rücker, C., & Rücker, G. (1992). Understanding the properties of isospectral points and pairs in graphs: The concept of orthogonal relation. Journal of Mathematical Chemistry, 9(3), 207-238. https://doi.org/10.1007/BF01165148

Vancouver

Rücker C, Rücker G. Understanding the properties of isospectral points and pairs in graphs: The concept of orthogonal relation. Journal of Mathematical Chemistry. 1992 Sept;9(3):207-238. doi: 10.1007/BF01165148

Bibtex

@article{59e3ffa5eb164305876ecf38e16654ae,
title = "Understanding the properties of isospectral points and pairs in graphs: The concept of orthogonal relation.",
abstract = "The mathematical property {"}orthogonal relationship{"} is used in proving the fact that isospectrality, isocodality and isocoefficiency of vertices within a graph are all equivalent. The same is true for isospectrality, {"}strict isocodality{"} and {"}strict isocoefficiency{"} of pairs (including edges) within a graph, whereas the {"}weak{"} versions of the latter properties are necessary but not sufficient for isospectrality of pairs. Similarly, necessary and sufficient conditions for isospectrality of vertices and pairs in different graphs are derived. In all these proofs, the concept of {"}orthogonal relation{"} plays a major role in that it allows the use of tools of elementary linear algebra.",
keywords = "Chemistry",
author = "Christoph R{\"u}cker and Gerta R{\"u}cker",
year = "1992",
month = sep,
doi = "10.1007/BF01165148",
language = "English",
volume = "9",
pages = "207--238",
journal = "Journal of Mathematical Chemistry",
issn = "0259-9791",
publisher = "Springer Netherlands",
number = "3",

}

RIS

TY - JOUR

T1 - Understanding the properties of isospectral points and pairs in graphs

T2 - The concept of orthogonal relation.

AU - Rücker, Christoph

AU - Rücker, Gerta

PY - 1992/9

Y1 - 1992/9

N2 - The mathematical property "orthogonal relationship" is used in proving the fact that isospectrality, isocodality and isocoefficiency of vertices within a graph are all equivalent. The same is true for isospectrality, "strict isocodality" and "strict isocoefficiency" of pairs (including edges) within a graph, whereas the "weak" versions of the latter properties are necessary but not sufficient for isospectrality of pairs. Similarly, necessary and sufficient conditions for isospectrality of vertices and pairs in different graphs are derived. In all these proofs, the concept of "orthogonal relation" plays a major role in that it allows the use of tools of elementary linear algebra.

AB - The mathematical property "orthogonal relationship" is used in proving the fact that isospectrality, isocodality and isocoefficiency of vertices within a graph are all equivalent. The same is true for isospectrality, "strict isocodality" and "strict isocoefficiency" of pairs (including edges) within a graph, whereas the "weak" versions of the latter properties are necessary but not sufficient for isospectrality of pairs. Similarly, necessary and sufficient conditions for isospectrality of vertices and pairs in different graphs are derived. In all these proofs, the concept of "orthogonal relation" plays a major role in that it allows the use of tools of elementary linear algebra.

KW - Chemistry

UR - http://www.scopus.com/inward/record.url?scp=0001478710&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/8fb66a2e-ce9a-3140-8323-9da8303d4d8a/

U2 - 10.1007/BF01165148

DO - 10.1007/BF01165148

M3 - Journal articles

VL - 9

SP - 207

EP - 238

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

SN - 0259-9791

IS - 3

ER -

Other publications by the same author(s)

Are Si-C bonds cleaved by microorganisms? A critical review on biodegradation of methylsiloxanes

Rücker, C., Grabitz, E. & Kümmerer, K., 01.04.2023, In: Chemosphere. 321, 137858.

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

Are Si–C bonds formed in the environment and/or in technical microbiological systems?

Rücker, C., Winkelmann, M. & Kümmerer, K., 08.2023, In: Environmental Science and Pollution Research. 30, 39, p. 91492-91500 9 p.

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

REACH und QSAR: ein Leitfaden für kleine und mittlere Unternehmen

Rücker, C., Mahmoud, W. M. M., Kümmerer, K. & Zipperer, U. (Editor), 06.2015, Lüneburg: Leuphana Universität Lüneburg, 29 p.

Research output: Working paper › Project reports › Research

Comment on "nomenclature, Chemical Abstracts Service Numbers, Isomer Enumeration, Ring Strain, and Stereochemistry: What Does Any of This Have to Do with an International Chemical Disarmament and Nonproliferation Treaty?"

Rücker, C., Meringer, M. & Wassermann, A., 13.04.2021, In: Journal of Chemical Education. 98, 4, p. 1465-1467 3 p.

Research output: Journal contributions › Comments / Debate / Reports › Research

Octanol-Water Partition Coefficient Measurement by a Simple 1H NMR Method

Cumming, H. & Rücker, C., 30.09.2017, In: ACS Omega. 2, 9, p. 6244-6249 6 p.

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

DOI

Recently viewed

Activities

  1. Available data on readily biodegradable ionic liquids
  2. Study of digital morphing tools in the architectural design process
  3. „Regional Conflicts & Contested Spatial Identities in the Digital Sphere”
  4. Universität Oxford
  5. IECER 2008
  6. HyperKult XVIII - Computer als Medium: The Cloud
  7. Unpacking multiple levels of governance in participatory environmental decision-making (with O. Fritsch)
  8. College (Organisation)
  9. Guidance on the application of in silico tools for Benign by Design
  10. The English Academy (Externe Organisation)
  11. Comparing responses of carbon dyamics to elevated atmosperic CO2 concentrations in arable crop rotations in Germany and China
  12. Land and Sea - 2009
  13. Università di Macerata
  14. Workshop on the Exploration of Low Temperature Plasma Physics - WELTPP 2017
  15. Policy Briefing 4
  16. EAWOP Small Group Meeting - 2011
  17. HyperImage – Bildorientierte E-Science-Netzwerke
  18. Schulleitung in Zeiten der Krise: Heraus- oder doch Überforderung? (Discussant)
  19. Under Which Conditions Does Public Participation Really Advance Sustainability Goals? Findings of a Meta-Analysis of Stakeholder Involvement in Environmental Decision-making (with O. Fritsch)

Publications

  1. Effects of an expressive writing intervention (EWI) with women treated for breast cancer explored with recurrence quantification analysis (RQA) of changes in text structure - a proof-of-concept study
  2. E-privacy concerns
  3. Web 2.0 Tasks in Action
  4. Non-technical success factors for bioenergy projects-Learning from a multiple case study in Japan
  5. Is the market classification of risk always efficient?
  6. German Utilities and Distributed PV
  7. TANGO: A reliable, open-source, browser-based task to assess individual differences in gaze understanding in 3 to 5-year-old children and adults
  8. Optimal scheduling for Automated Guided Vehicles (AGV) in blocking job-shops
  9. Categorizing urban tasks
  10. Do Linguistic Features Influence Item Difficulty in Physics Assessments?
  11. Electrical and Mechanical Characterization of Polymer Nanofibers for Sensor Application
  12. Methods and compositions relating to a vaccine against prostate cancer
  13. Firm size and the use of export intermediaries.
  14. Planning for Sea Spaces I
  15. Artificial Intelligence as a cultural technique
  16. A microsystem for growth inhibition test of Enterococcus faecalis based on impedance measurement
  17. Einführung in die systemnahe Programmierung
  18. A control strategy for electromagnetic near and far field calculation
  19. What if this was a piece of art
  20. A new method for collecting agile tiger beetles by live pitfall trapping
  21. Gamen
  22. Structuring Sustainability Reports for Environmental Standards with LLMs guided by Ontology
  23. Variational pragmatics
  24. HAWK@QALD5 - Trying to answer hybrid questions with various simple ranking techniques
  25. Construction of Container Terminal 4
  26. Digitale Transformation, quo vadis?
  27. Von Differenz zu Vielfalt zu Super-Diversity
  28. Testing Lazear's Jack-of-all-trades
  29. Looking at Figures and Fabrics with a ‘Period Eye’