1.1.2. Examples of Euler Circuit and Path

Try these first

1. 1.

   Define an Euler circuit.

   Hint

   Remember that it ends where it starts.

2. 2.

   What is an Euler path?

   Hint

   Think of starting at one point and finishing at another.

3. 3.

   What is required for a graph to have an Euler circuit?

   • At least two odd degree vertices
   • All vertices have even degrees
   • At least one vertex with odd degree

   Hint

   Think about what makes a circuit.

4. 4.

   True or False: An Euler Path can have more than two odd degree vertices.

   • True
   • False

   Hint

   Consider the definition of odd vertices.

5. 5.

   Design a graph with an Euler circuit and illustrate it.

   Hint

   Try using simple shapes, like squares.

6. 6.

   Create a graph with no Euler path or circuit and explain why.

   Hint

   Draw several parts and tally the odd vertices.