Eulerian Path Analysis: Is My Figure Drawable?

  • Thread starter Krypt0s
  • Start date
  • Tags
    Path
In summary, Krypt0s used graph theory to analyze a graph and found that it has four nodes with an odd degree. They then used a theorem to prove that the graph does not have an Eulerian path. Despite some confusion about the analysis, it was determined that Krypt0s' approach was correct.
Physics news on Phys.org
  • #2
Pardon me, but I don't see any analysis. All I see is a copy of the proof.
 
  • #3
What you did is fine, Krypt0s.

farleyknight said:
Pardon me, but I don't see any analysis.
Krypt0s analyzed the graph in question and found four nodes in this particular graph that have an odd degree.
All I see is a copy of the proof.
Are we looking at the same page? Krypt0s used the theorem to prove the particular graph in question has no Eulerian path. What's wrong with that?
 
  • #4
D H said:
What you did is fine, Krypt0s.


Krypt0s analyzed the graph in question and found four nodes in this particular graph that have an odd degree.

Are we looking at the same page? Krypt0s used the theorem to prove the particular graph in question has no Eulerian path. What's wrong with that?

I was looking at the text, not the graph.
 
  • #5
I was looking at the text, too. All that is needed to prove that the graph in question has no Eulerian path is to (a) cite the relevant theorem and (b) show that the relevant conditions for lack of an Eulerian path apply. He did both.
 

1. What is Eulerian Path Analysis?

Eulerian Path Analysis is a mathematical method used to determine whether a graph or network can be drawn without lifting the pen or retracing any lines. It is named after the Swiss mathematician Leonhard Euler, who first described the concept in the 18th century.

2. How is Eulerian Path Analysis used in scientific research?

Eulerian Path Analysis is commonly used in network analysis and graph theory to study complex systems, such as social networks, transportation systems, and biochemical pathways. It can also be applied in areas such as computer science, genetics, and epidemiology to analyze data and identify patterns.

3. What is the difference between an Eulerian Path and an Eulerian Circuit?

An Eulerian Path is a path that visits every edge in a graph exactly once, while an Eulerian Circuit is a path that starts and ends at the same vertex and visits every edge in a graph exactly once. In other words, an Eulerian Circuit is a closed Eulerian Path.

4. How do you determine if a figure is drawable using Eulerian Path Analysis?

To determine if a figure is drawable, you need to analyze the number of vertices with odd degrees. If there are more than two vertices with odd degrees, the figure is not drawable. If there are exactly two vertices with odd degrees, the figure is drawable, and the path will start at one of the odd-degree vertices and end at the other.

5. Is Eulerian Path Analysis the only method for determining if a figure is drawable?

No, there are other methods for determining if a figure is drawable, such as Fleury's algorithm and Hierholzer's algorithm. However, Eulerian Path Analysis is the most commonly used method due to its simplicity and effectiveness.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
353
  • Differential Equations
Replies
1
Views
944
Replies
7
Views
1K
  • Topology and Analysis
Replies
25
Views
3K
  • STEM Academic Advising
Replies
3
Views
872
  • Differential Equations
Replies
1
Views
993
  • Classical Physics
Replies
18
Views
1K
  • STEM Academic Advising
Replies
8
Views
1K
Replies
6
Views
1K
  • Science and Math Textbooks
Replies
20
Views
2K
Back
Top