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 Concept Videos

Hückel's Rule Diagram of π MOs: Frost Circle01:08

Hückel's Rule Diagram of π MOs: Frost Circle

6.1K
The Frost circle or the inscribed polygon method is a graphical method for determining the relative energies of π molecular orbitals (MOs) for planar, fully conjugated, and monocyclic compounds. This method was first described by A. A. Frost and Boris Musulin in 1953.
A Frost circle is constructed by drawing a polygon whose number of edges is equal to the number of carbons of the given cyclic system, with one of the vertices pointing down. Then, a circle is drawn enclosing the polygon so that...
6.1K
Graphs of Polar Equations01:17

Graphs of Polar Equations

378
The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...
378
Frost Circles for Different Conjugated Systems01:18

Frost Circles for Different Conjugated Systems

4.1K
The inscribed polygon method is consistent with Hückel’s 4n + 2 rule and helps to learn whether the given cyclic compound is aromatic or not. The compound is stable and aromatic if every bonding molecular orbital (MO) is completely filled with a pair of electrons. However, if the non-bonding or antibonding orbitals are filled with electrons, the compound is unstable and not aromatic. Consider the Frost circle diagrams for cycloalkenes containing 4 to 8 carbons.
4.1K
Molecular Shape and Polarity03:37

Molecular Shape and Polarity

76.9K
Dipole Moment of a Molecule
76.9K
Molecular Geometry and Dipole Moments02:36

Molecular Geometry and Dipole Moments

19.9K
The VSEPR theory can be used to determine the electron pair geometries and molecular structures as follows:
19.9K
Valence Bond Theory02:42

Valence Bond Theory

11.5K
Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
11.5K

You might also read

Related Articles

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

Sort by
Same author

Retraction notice to "Molecular targets for the management of cancer using Curcuma longa Linn. phytoconstituents: A Review" [Biomedicine & Pharmacotherapy 135 (2021) 111078].

Biomedicine & pharmacotherapy = Biomedecine & pharmacotherapie·2026
Same author

Non-ICANS Neurologic Events in Patients With Relapsed/Refractory Multiple Myeloma Treated With Ciltacabtagene Autoleucel: Clinical Presentation and Management in CARTITUDE Studies.

Clinical lymphoma, myeloma & leukemia·2026
Same author

In vitro and in vivo investigations of antibacterial B-TCP/polymer composite enhanced with strontium for bone grafting and photocatalytic applications.

Cytotechnology·2026
Same author

Colorectal Cancer Screening Knowledge and Associated Willingness and Barriers to Screening in Nationwide Pakistan Cohort.

Euroasian journal of hepato-gastroenterology·2026
Same author

Solvent-Dependent Bioactive Composition and Antifungal Potential of Neem (Azadirachta indica) Seed Extracts Against Mycotoxigenic Aspergillus Species.

Chemistry & biodiversity·2026
Same author

Synthesis of silver nanoparticles via eco-friendly green chemistry from Fragaria nubicola.

Pakistan journal of pharmaceutical sciences·2026
Same journal

In-silico combinatorial design and pharmacophore modeling of potent antimalarial 4-anilinoquinolines utilizing QSAR and computed descriptors.

SpringerPlus·2017
Same journal

Erratum to: Implication of Paris Agreement in the context of long-term climate mitigation goals.

SpringerPlus·2017
Same journal

Erratum to: Associations between adherence, depressive symptoms and health-related quality of life in young adults with cystic fibrosis.

SpringerPlus·2017
Same journal

Erratum to: Numerical method to compute acoustic scattering effect of a moving source.

SpringerPlus·2017
Same journal

Identifying appropriate protected areas for endangered fern species under climate change.

SpringerPlus·2017
Same journal

An Algorithm to detect balancing of iterated line sigraph.

SpringerPlus·2017
See all related articles

Related Experiment Video

Updated: Mar 14, 2026

Author Spotlight: Non-Invasive Imaging of Complex Bio-Structures Using Polarization-Sensitive Two-Photon Microscopy
05:54

Author Spotlight: Non-Invasive Imaging of Complex Bio-Structures Using Polarization-Sensitive Two-Photon Microscopy

Published on: September 8, 2023

2.0K

On m-polar fuzzy graph structures.

Muhammad Akram1, Rabia Akmal1, Noura Alshehri2

  • 1Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan.

Springerplus
|September 22, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces m-polar fuzzy graphs, enhancing network models with greater precision and flexibility than traditional fuzzy systems. These new structures offer improved data representation for complex, multi-attribute information.

Keywords:
Cartesian productCompositionCross productJoinLexicographic productStrong productUnion of two m-PFGSsm-Polar fuzzy graph structure (m-PFGSs)

More Related Videos

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients
09:32

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients

Published on: December 18, 2016

13.0K
Generating Strictly Controlled Stimuli for Figure Recognition Experiments
05:39

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

5.6K

Related Experiment Videos

Last Updated: Mar 14, 2026

Author Spotlight: Non-Invasive Imaging of Complex Bio-Structures Using Polarization-Sensitive Two-Photon Microscopy
05:54

Author Spotlight: Non-Invasive Imaging of Complex Bio-Structures Using Polarization-Sensitive Two-Photon Microscopy

Published on: September 8, 2023

2.0K
Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients
09:32

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients

Published on: December 18, 2016

13.0K
Generating Strictly Controlled Stimuli for Figure Recognition Experiments
05:39

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

5.6K

Area of Science:

  • Graph Theory
  • Fuzzy Set Theory
  • Network Modeling

Background:

  • Classical and fuzzy models struggle with multi-attribute, multi-polar information.
  • Existing models lack the precision and flexibility for complex network data.
  • There is a need for advanced mathematical structures to represent uncertainty.

Purpose of the Study:

  • Introduce the concept of m-polar fuzzy graph structures.
  • Define and explore various operations on these structures.
  • Analyze the properties of m-polar fuzzy graphs.

Main Methods:

  • Definition of m-polar fuzzy graph structures.
  • Introduction of operations: Cartesian product, strong product, cross product, lexicographic product, composition, union, and join.
  • Illustrative examples and property analysis.

Main Results:

  • Established the framework for m-polar fuzzy graph structures.
  • Demonstrated the utility of defined operations through examples.
  • Investigated key properties inherent to these structures.

Conclusions:

  • m-polar fuzzy graphs provide a more precise and flexible framework for network models.
  • The introduced operations are fundamental for manipulating and analyzing these complex structures.
  • This research advances the application of fuzzy set theory in network analysis.