Enrol to start learning
Reading is open to everyone. Enrolling is free, and it is what unlocks the audio lessons, practice tests and progress tracking.
1. Euler Path and Euler Circuit
The lecture provides an in-depth exploration of Euler paths and Euler circuits, defining their characteristics and conditions for existence in graphs. The presentation includes examples illustrating both concepts, proving necessary and sufficient conditions, and demonstrating Fleury’s algorithm for finding Euler circuits. Additionally, it characterizes Euler paths, highlighting the differences between paths and circuits within the context of graph theory.
Sections
This section presents the definitions and characteristics of Euler paths and circuits in graphs, including necessary and sufficient conditions for their existence.
Fleury's Algorithm is a method to find Euler circuits in graphs, ensuring optimal edge traversal without duplicating edges.
An Euler circuit visits every edge of a graph exactly once and returns to the starting vertex.
An Euler path visits every edge exactly once but does not return to the starting vertex.
Graphs can have Euler circuits if all vertices have even degrees, or Euler paths if exactly two vertices have odd degrees.
Euler Circuit
A closed trail in a graph that visits every edge once and returns to the starting vertex.
Euler Path
A trail in a graph that visits every edge once but does not return to the starting vertex.
Fleury’s Algorithm
An algorithm used to find an Euler circuit in a graph by avoiding 'cut' edges until necessary.
Even Degree
A vertex has an even degree if it is connected to an even number of edges.
Odd Degree
A vertex has an odd degree if it is connected to an odd number of edges.
Practice Exercises
Total Questions
2
Estimated Time
4 min
Passing Score
70%
Instructions
- Read each question carefully
- You can use hints if you need help
- Complete all questions before submitting
1 more question available
Enrol free