Euler Circuits and Paths

Front

What is an Euler Path?

Back

An Euler Path is a trail in a graph that visits every edge exactly once but may start and end at different vertices.

Front

What is an Euler Circuit?

Back

An Euler Circuit is a trail in a graph that visits every edge exactly once and starts and ends at the same vertex.

Front

What is the starting and ending point of an Euler Circuit?

Back

An Euler Circuit starts and ends at the same vertex.

Front

What is the starting and ending point of an Euler Path?

Back

An Euler Path starts and ends at different vertices.

Front

Can an Euler Circuit exist in a graph with odd degree vertices?

Back

No, an Euler Circuit can only exist in a graph where all vertices have even degrees.

Front

Can an Euler Path exist in a graph with odd degree vertices?

Back

Yes, an Euler Path can exist in a graph with exactly two vertices of odd degree.

Front

What is the degree of a vertex in a graph?

Back

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

Front

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

Back

A graph must be connected and all vertices must have even degrees.

Front

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

Back

A graph must be connected and have exactly zero or two vertices of odd degree.

Front

Identify the Euler Circuit: KLQPQOKLOMK, KLQMPQOKNLOMK, KLQMPQOK, KMOLNKOQMK

Back

KLQMPQOKNLOMK is the Euler Circuit.