Euler Paths and Circuits

Front

What is an Euler Circuit?

Back

An Euler Circuit is a path in a graph that visits every edge exactly once and returns to the starting vertex.

Front

What is an Euler Path?

Back

An Euler Path is a path in a graph that visits every edge exactly once but does not necessarily return to the starting vertex.

Front

True or False: A graph with all vertices of even degree has an Euler Circuit.

Back

True

Front

True or False: A graph with exactly two vertices of odd degree has an Euler Path.

Back

True

Front

What is the relationship between Euler Paths and Euler Circuits?

Back

Some Euler Paths are also Euler Circuits, but not all.

Front

Complete the sentence: ALL, SOME or NO - ______ graphs with exactly 0 odd vertices have at least one Euler path.

Back

ALL

Front

Complete the sentence: ALL, SOME or NO - ______ paths are Euler Paths.

Back

SOME

Front

Complete the sentence: ALL, SOME or NO - ______ Euler paths are Euler Circuits.

Back

SOME

Front

What is the degree of a vertex?

Back

The degree of a vertex is the number of edges incident to it.

Front

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

Back

A graph must have all vertices of even degree to have an Euler Circuit.