1.1.1. Definition of Euler Circuit and Euler Path

Try these first

1. 1.

   Define an Euler Circuit.

   Hint

   Think about what 'circuit' means in relation to starting and ending.

2. 2.

   What is the necessary condition for a graph to have an Euler circuit?

   Hint

   Example: Look at the degrees of each vertex.

3. 3.

   What is an Euler Circuit?

   • Visits every edge exactly once
   • returns to the start
   • Visits every edge once but does not return
   • Visits some edges only

   Hint

   Consider the definition discussed in class.

4. 4.

   True or False: An Euler Path cannot have odd degree vertices.

   • True
   • False

   Hint

   Reflect on the conditions we reviewed.

5. 5.

   Construct your own graph that contains an Euler circuit and explain how you determined it qualified.

   Hint

   Consider the shape and connections of the graph.

6. 6.

   Find a real-world application for Euler circuits or paths and detail how they function in that context.

   Hint

   Think of transportation or delivery routes.