Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

On walks in molecular graphs.

I Gutman1, C Rücker, G Rücker

  • 1Faculty of Science, University of Kragujevac, P.O. Box 60, YU-34000 Kragujevac, Yugoslavia.

Journal of Chemical Information and Computer Sciences
|June 21, 2001
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

The role of routine SARS-CoV-2 screening of healthcare-workers in acute care hospitals in 2020: a systematic review and meta-analysis.

BMC infectious diseases·2022
Same author

Biopsy-derived oral keratinocytes - A model to potentially test for oral mucosa radiation sensitivity.

Clinical and translational radiation oncology·2022
Same author

Drugs for preventing postoperative nausea and vomiting in adults after general anaesthesia: an abridged Cochrane network meta-analysis.

Anaesthesia·2020
Same author

Impact of investigator initiated trials and industry sponsored trials on medical practice (IMPACT): rationale and study design.

BMC medical research methodology·2020
Same author

Differences in the placebo response between trials do not necessarily preclude network meta-analysis.

Acta psychiatrica Scandinavica·2018
Same author

Influence of experience and qualification on PET-based target volume delineation. When there is no expert--ask your colleague.

Strahlentherapie und Onkologie : Organ der Deutschen Rontgengesellschaft ... [et al]·2014
Same journal

Future Papers.

Journal of chemical information and computer sciences·2016
Same journal

Future Papers.

Journal of chemical information and computer sciences·2016
Same journal

Future Papers.

Journal of chemical information and computer sciences·2016
Same journal

Future Papers.

Journal of chemical information and computer sciences·2016
Same journal

Future Papers.

Journal of chemical information and computer sciences·2016
Same journal

Future Papers.

Journal of chemical information and computer sciences·2016
See all related articles

Molecular walk counts (MWC) and total walk counts (TWC) quantify organic molecule complexity. This study reveals linear dependencies between MWCs and their correlations with TWCs, linking them to graph eigenvalues and eigenvectors.

Area of Science:

  • Theoretical Chemistry
  • Graph Theory
  • Cheminformatics

Background:

  • Walks in molecular graphs and their counts are foundational in theoretical chemistry.
  • The (i, j)-entry of the kth power of the adjacency matrix represents walks of length k between vertices i and j.
  • Molecular walk counts (MWC) and total walk counts (TWC) have been proposed for QSPR studies and complexity measurement.

Purpose of the Study:

  • To establish general properties of molecular walk counts (MWC) and total walk counts (TWC).
  • To explore linear dependencies among MWCs and correlations between MWCs and TWCs.
  • To investigate connections between walk counts and spectral properties of molecular graphs.

Main Methods:

  • Analysis of molecular graph adjacency matrices and their powers.

Related Experiment Videos

  • Application of spectral decomposition techniques.
  • Characterization of graphs based on walk count properties.

    • Main Results:

    • Established linear dependence relationships among MWCs.
    • Demonstrated linear correlations between MWCs and TWCs.
    • Revealed spectral decomposition of MWCs and connections to eigenvalues and eigenvectors.
    • Characterized graphs with minimal and maximal walk counts.

    Conclusions:

    • MWCs and TWCs exhibit predictable mathematical properties, including linear dependencies and correlations.
    • Walk counts are intrinsically linked to the spectral properties (eigenvalues, eigenvectors) of molecular graphs.
    • These findings provide a deeper understanding of molecular complexity and graph-based descriptors for QSPR.