Graph Theory, Euler and Hamilton Circuits and Paths

Choose the correct term to match each definition: Lines or curves that connect vertices.

• Regions

• Vertices

• Edges

• Paths

Tags

CCSS.HSG.CO.A.1

Tracing all edges on a figure without picking up your pencil and repeating and starting and stopping in the same spot

• Euler Circuit
• Euler Path

Circuits start and stop at 

• same vertex
• different vertices

This graph will have a Euler's Circuit

• True
• False

How do we quickly determine if a graph will have a Euler's Circuit? 

• All even degree verticies
• Exactly 2 odd degree verticies
• Every Vertex will be used once
• I have no clue

Is the following graph connected or disconnected? Explain why or why not.

• Connected because all vertices are even.

• Connected because one can get from one vertex to every other vertex on the graph

• Disconnected because all vertices are even

• Disconnected because one can NOT get from one vertex to every other vertex.

Which of the graphs below have Euler circuits?

• I only

• II only

• Both I and II

• Neither I and II

Which of the graphs below have Euler circuits?

• I only

• II only

• Both I and II

• Neither I and II

Which of the graphs below have Euler circuits?

• I only

• II only

• Both I and II

• Neither I or II

What is the valence of vertex A in the graph ?

• 3

• 5

• 7

• 11