Graph Theory Vocabulary

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

What is a connected graph?

Back

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

Front

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

Back

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

Front

What is the 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.

Front

What does it mean for a vertex to have an odd degree?

Back

A vertex has an odd degree if the number of edges connected to it is odd.

Front

What does it mean for a vertex to have an even degree?

Back

A vertex has an even degree if the number of edges connected to it is even.

Front

Can a graph have both an Euler Circuit and an Euler Path?

Back

Yes, if a graph has an Euler Circuit, it also has an Euler Path.

Front

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

Back

Euler's Theorems provide conditions under which a graph can have Euler Circuits and Euler Paths.

Front

What is a trail in graph theory?

Back

A trail is a walk in a graph that does not repeat any edges.