Euler Path & Circuit

Front

What is an Euler Path?

Back

An Euler Path is a trail in a graph that visits every edge exactly once but may visit vertices more than once.

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.

Front

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

Back

A graph has an Euler Circuit if all vertices have even degrees and the graph is connected.

Front

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

Back

A graph has an Euler Path if it has exactly zero or two vertices of odd degree and the graph is connected.

Front

Can a graph with all vertices of odd degree have an Euler Circuit?

Back

No, a graph with all vertices of odd degree cannot have an Euler Circuit.

Front

What does it mean for a graph to be connected?

Back

A graph is connected if there is a path between every pair of vertices.

Front

If a graph has more than two vertices of odd degree, what can be said about its Euler Path or Circuit?

Back

If a graph has more than two vertices of odd degree, it has neither an Euler Path nor an Euler Circuit.

Front

What is the difference between an Euler Path and an Euler Circuit?

Back

An Euler Path does not need to return to the starting vertex, while an Euler Circuit must return to the starting vertex.

Front

Can a disconnected graph have an Euler Path or Circuit?

Back

No, a disconnected graph cannot have an Euler Path or Circuit.

Front

What is the significance of Euler's Theorem in graph theory?

Back

Euler's Theorem provides the conditions under which a graph can have Euler Paths and Circuits.