1.1.3. Characterization of Euler Circuit

Try these first

1. 1.

   Define an Euler circuit?

   Hint

   Think of circuits starting from a point and returning.

2. 2.

   What condition must be met for Euler paths?

   Hint

   Consider the implications of starting and ending points.

3. 3.

   What is an Euler Circuit?

   • A path covering all vertices
   • A path that loops back
   • A circuit covering each edge exactly once

   Hint

   Think about how circuits function.

4. 4.

   True or False: An Euler path can only exist if all vertices have odd degrees.

   • True
   • False

   Hint

   Consider the requirements for paths and circuits.

5. 5.

   Given a graph structure with vertices of degrees 3, 3, 2, 2, and 4, determine if an Euler path exists and justify your answer.

   Hint

   Count the vertices with odd degrees.

6. 6.

   Using Fleury's algorithm, demonstrate how to find an Euler circuit in the given graph: A-B, B-C, C-D, D-A, A-C.

   Hint

   Ensure you explain each choice when picking edges.