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

Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

15.4K
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
15.4K
Castigliano's Theorem01:18

Castigliano's Theorem

604
Castigliano's theorem analyzes displacements and rotations in elastic structures. It relates the derivative of elastic strain energy to the applied forces or moments, allowing for the calculation of deformations. The theorem states that the partial derivative of the total strain energy of a system with respect to a specific load results in the displacement at the point where the load is applied. This principle applies to both forces and moments.
604
Circuit Terminology01:14

Circuit Terminology

2.4K
An electrical network is a system composed of interconnected elements, such as resistors, capacitors, inductors, and voltage or current sources. Unlike a circuit, an electrical network does not necessarily form a closed path. In other words, while all circuits can be considered networks due to their interconnected nature, not every network qualifies as a circuit.
A circuit, on the other hand, is also an interconnected system of electrical elements but must contain one or more closed paths.
2.4K
First-Order Circuits01:15

First-Order Circuits

2.4K
First-order electrical circuits, which comprise resistors and a single energy storage element - either a capacitor or an inductor, are fundamental to many electronic systems. These circuits are governed by a first-order differential equation that describes the relationship between input and output signals.
One common example of a first-order circuit is the RC (resistor-capacitor) circuit. These circuits are used in relaxation oscillators such as neon lamp oscillator circuits. When voltage is...
2.4K
Reynolds Transport Theorem01:24

Reynolds Transport Theorem

1.4K
The Reynolds transport theorem provides a framework to relate the time rate of change of an extensive property within a system to that in a control volume, which is crucial for analyzing fluid dynamics. Extensive properties, such as mass, velocity, acceleration, temperature, and momentum, can be expressed in terms of the mass of a fluid portion. These properties are called extensive because they depend on the system's size, while intensive properties are their corresponding values per unit...
1.4K
Second-Order Circuits01:17

Second-Order Circuits

1.8K
Integrating two fundamental energy storage elements in electrical circuits results in second-order circuits, encompassing RLC circuits and circuits with dual capacitors or inductors (RC and RL circuits). Second-order circuits are identified by second-order differential equations that link input and output signals.
Input signals typically originate from voltage or current sources, with the output often representing voltage across the capacitor and/or current through the inductor. For example, in...
1.8K

You might also read

Related Articles

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

Sort by
Same author

On the Decomposition of Vertex-Transitive Graphs into Multicycles.

Journal of research of the National Bureau of Standards (1977)·2021
Same author

Secure spread spectrum watermarking for multimedia.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·1997
See all related articles

Related Experiment Video

Updated: Oct 19, 2025

Analyzing the Size, Shape, and Directionality of Networks of Coupled Astrocytes
10:10

Analyzing the Size, Shape, and Directionality of Networks of Coupled Astrocytes

Published on: October 4, 2018

9.0K

Circulants and the Characterization of Vertex-Transitive Graphs.

F T Leighton1

  • 1Massachusetts Institute of Technology, Cambridge, MA 02139.

Journal of Research of the National Bureau of Standards (1977)
|September 27, 2021
PubMed
Summary

Researchers introduce multidimensional circulants, a new class of vertex-transitive graphs. These graphs are precisely those with an automorphism group containing a regular abelian subgroup, extending the concept of circulant graphs.

Keywords:
circulantmultidimensional circulantpoint-symmetricregular groupstarred polygonvertex-transitive

More Related Videos

Viral Tracing of Genetically Defined Neural Circuitry
13:06

Viral Tracing of Genetically Defined Neural Circuitry

Published on: October 17, 2012

18.7K
Generating Strictly Controlled Stimuli for Figure Recognition Experiments
05:39

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

5.4K

Related Experiment Videos

Last Updated: Oct 19, 2025

Analyzing the Size, Shape, and Directionality of Networks of Coupled Astrocytes
10:10

Analyzing the Size, Shape, and Directionality of Networks of Coupled Astrocytes

Published on: October 4, 2018

9.0K
Viral Tracing of Genetically Defined Neural Circuitry
13:06

Viral Tracing of Genetically Defined Neural Circuitry

Published on: October 17, 2012

18.7K
Generating Strictly Controlled Stimuli for Figure Recognition Experiments
05:39

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

5.4K

Area of Science:

  • Graph theory
  • Combinatorics
  • Algebraic graph theory

Background:

  • Circulant graphs are a well-studied class of vertex-transitive graphs.
  • Understanding the structure of vertex-transitive graphs is a fundamental problem in graph theory.

Purpose of the Study:

  • To generalize the concept of circulant graphs to a wider class of graphs.
  • To characterize vertex-transitive graphs based on their automorphism groups.

Main Methods:

  • Extension of the definition of circulant graphs.
  • Utilizing Sabidussi's theorem on vertex-transitive graphs and transitive subgroups.
  • Application of group theory, specifically regular abelian subgroups.

Main Results:

  • Introduction of the class of multidimensional circulant graphs.
  • Demonstration that multidimensional circulants are precisely vertex-transitive graphs with a regular abelian subgroup.
  • A simplified proof of Turner's theorem on circulant graphs with a prime number of nodes.

Conclusions:

  • Multidimensional circulants provide a broader framework for studying vertex-transitive graphs.
  • The characterization offers new insights into the relationship between graph structure and symmetry.
  • The methods facilitate proofs for related theorems in graph theory.