1.1.4. Characterization of Euler Path

Try these first

1. 1.

   What is an Euler circuit?

   Hint

   Think about the starting and ending vertex.

2. 2.

   How many vertices must have an odd degree for an Euler path?

   Hint

   Remember the acronym 'DOUBLE O'.

3. 3.

   How many vertices need to have odd degrees for an Euler path?

   • None
   • One
   • Two
   • Three

   Hint

   Recall the conditions for Euler paths.

4. 4.

   True or False: All vertices of a graph must have even degree for an Euler circuit.

   • True
   • False

   Hint

   Think about the definitions you've learned.

5. 5.

   Given this graph structure: A-B (odd), B-C (even), C-D (even), D-E (odd), analyze and conclude if Euler paths or circuits are possible.

   Hint

   Check the degree of each vertex.

6. 6.

   Design an original network that can effectively demonstrate an Euler circuit. What conditions will your graph need?

   Hint

   Try to balance the edges for vertices.