Euler Circuits and Paths

This lesson introduces Fleury's Algorithm, a method to find Euler circuits and paths in graphs. It explains the conditions for a graph to have an Euler circuit and provides a step-by-step guide to applying the algorithm. An example is given to demonstrate the process, highlighting key decisions and considerations. The lesson concludes with a summary of the algorithm's application.

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

• The graph is connected.

• All vertices have even degree.

• All vertices have odd degree.

• The graph is a tree.

In Fleury's Algorithm, where do you start if you are finding an Euler path?

• Any vertex with even degree.

• Any vertex with odd degree.

• One of the two vertices with odd degree.

• The vertex with the highest degree.

What is the first step in Fleury's Algorithm when finding an Euler circuit?

• List all edges.

• Check if the graph is connected.

• Start at any vertex.

• Choose any edge to start.

After deleting edge AB, which vertex do you move to next?

• Vertex C

• Vertex A

• Vertex B

• Vertex D

Why can't you delete edge EA in the example provided?

• It would create a loop.

• It would separate the graph into two disconnected sets.

• It is not part of the circuit.

• It is the only edge left.

What should you do if deleting an edge would separate the graph?

• Delete it anyway.

• Choose another edge.

• Add a new edge.

• Start over.

What is the sequence of edges deleted after reaching vertex D?

• DA, AB, BC, CD

• DC, CB, BE, EA

• DC, CE, EB, AD

• DE, EC, CB, BA

What is the final vertex reached in the example circuit?

• Vertex F

• Vertex B

• Vertex G

• Vertex A

Which edge is deleted last in the example?

• Edge FG

• Edge GA

• Edge AF

• Edge AB

What is the final sequence of vertices in the Euler circuit?

• A, D, C, B, E, A, F, G, A

• A, B, C, D, E, F, G, A

• A, C, D, E, B, A, F, G, A

• A, B, E, D, C, B, E, A, F, G, A