Types of walks (trails, paths, circuits, cycles, etc.)

A walk is...

• Any route along a graph

• A route with no repeated edges

• A route with no repeated vertices

• A route which starts and ends at the same vertex

A path...

(tick all that apply)

• Has no repeated edges

• Has no repeated vertices

• Starts/ends at the same vertex

• Uses every edge

• Uses every vertex

A circuit...

(tick all that apply)

• Has no repeated edges

• Has no repeated vertices

• Starts/ends at the same vertex

• Uses every edge

• Uses every vertex

A trail...

(tick all that apply)

• Has no repeated edges

• Has no repeated vertices

• Starts/ends at the same vertex

• Uses every edge

• Uses every vertex

A cycle...

(tick all that apply)

• Has no repeated edges

• Has no repeated vertices

• Starts/ends at the same vertex

• Uses every edge

• Uses every vertex

A path...

(tick all that apply)

• Has no repeated edges

• Has no repeated vertices

• Starts/ends at the same vertex

• Uses every edge

• Uses every vertex

An Eulerian trail...

(tick all that apply)

• Has no repeated edges

• Has no repeated vertices

• Starts/ends at the same vertex

• Uses every edge

• Uses every vertex

A Hamiltonian cycle...

(tick all that apply)

• Has no repeated edges

• Has no repeated vertices

• Starts/ends at the same vertex

• Uses every edge

• Uses every vertex

A Hamiltonian path...

(tick all that apply)

• Has no repeated edges

• Has no repeated vertices

• Starts/ends at the same vertex

• Uses every edge

• Uses every vertex

An Eulerian circuit...

(tick all that apply)

• Has no repeated edges

• Has no repeated vertices

• Starts/ends at the same vertex

• Uses every edge

• Uses every vertex