Graph Theory Vocabulary

A point on a graph

• Vertex

• Edge

• Path

• Circuit

A line or curve that connects vertices on a graph

• vertex

• edge

• degree

• path

A trail through a graph that uses every edge once and begins and ends at a different vertex

• Hamitonian Path

• HAmiltonian Circuit

• Euler Path

• Euler Circuit

A trail through a graph that uses every edge once and begins and ends at the same vertex

• Hamiltonian Path

• Hamiltonian Circuit

• Euler Path

• Euler Circuit

A trail through a graph that uses every vertex once and begins and ends at a different vertex

• Hamiltonian Path

• Hamiltonian Circuit

• Euler Path

• Euler Circuit

A trail through a graph that uses every vertex once and begins and ends at the same vertex

• Hamiltonian Circuit

• Hamiltonian Path

• Euler Path

• Euler Circuit

The number of edges connected to a vertex

• Euler's Shortcut

• Euler Path

• Euler Circuit

• degree

A trail within a graph that starts and ends at the same vertex

• Euler Path

• degree

• cycle

• edge