Paths and Cycles

What is a walk in graph theory?

• A sequence of connected vertices

• A walk with no repeated edges

• A walk with no repeated vertices

• A walk that starts and finishes at the same vertex

What defines a trail in graph theory?

• A walk with no repeated edges

• A walk with no repeated vertices

• A walk that starts and finishes at the same vertex

• A sequence of connected vertices

What is a closed trail?

• A walk with no repeated edges that starts and finishes at the same vertex

• A walk with no repeated vertices

• A walk with repeated edges

• A sequence of connected vertices

What is a path in graph theory?

• A walk with no repeated edges and no repeated vertices

• A walk with repeated edges

• A walk that starts and finishes at the same vertex

• A sequence of connected vertices

What is a cycle in graph theory?

• A walk with no repeated edges and no repeated vertices that starts and finishes at the same vertex

• A walk with repeated edges

• A walk with no repeated vertices

• A sequence of connected vertices

What is an Eulerian trail?

• A walk with no repeated edges that includes every edge in a graph

• A walk with repeated edges

• A walk with no repeated vertices

• A sequence of connected vertices

When does an open Eulerian trail exist?

• When the graph has exactly two vertices of odd degree

• When the graph has all vertices of even degree

• When the graph has no repeated edges

• When the graph is a sequence of connected vertices

How do you find an Eulerian trail?

• Start at one of the two vertices of odd degree and finish at the other vertex of odd degree

• Start and finish at the same vertex

• Walk with no repeated edges

• Walk with no repeated vertices

What is a closed Eulerian trail?

• A walk with no repeated edges that includes every edge in a graph and starts and finishes at the same vertex

• A walk with repeated edges

• A walk with no repeated vertices

• A sequence of connected vertices

When does a closed Eulerian trail exist?

• When the graph has all vertices of even degree

• When the graph has exactly two vertices of odd degree

• When the graph has no repeated edges

• When the graph is a sequence of connected vertices