AMDM - Unit 4 Test Part I

Front

What is an Euler Path?

Back

An Euler Path is a trail in a graph that visits every edge exactly once. It exists if there are exactly two vertices of odd degree.

Front

What is an Euler Circuit?

Back

An Euler Circuit is a trail in a graph that visits every edge exactly once and returns to the starting vertex. It exists if all vertices have even degree.

Front

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

Back

A graph will have an Euler Path if it has exactly two vertices of odd degree.

Front

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

Back

A graph will have an Euler Circuit if all vertices have even degree.

Front

What is a Hamiltonian Circuit?

Back

A Hamiltonian Circuit is a cycle in a graph that visits every vertex exactly once and returns to the starting vertex.

Front

What is a Hamiltonian Path?

Back

A Hamiltonian Path is a trail in a graph that visits every vertex exactly once.

Front

What does it mean if a graph has one odd vertex?

Back

If a graph has one odd vertex, it will have an Euler Path but not an Euler Circuit.

Front

What is the significance of vertex degree in graph theory?

Back

The degree of a vertex is the number of edges connected to it. It determines the existence of Euler Paths and Circuits.

Front

Can a graph with more than two odd vertices have an Euler Path?

Back

No, a graph with more than two odd vertices will never have an Euler Path or Circuit.

Front

What is the relationship between vertex degrees and Eulerian graphs?

Back

In Eulerian graphs, all vertices must have even degrees for an Euler Circuit, while exactly two odd degrees allow for an Euler Path.