12Applications Graph theory

Graphs that have directed edges are called

• multiple edges

• simple graphs

• digraphs

• trees

A sequence of vertices for which each vertex in the sequence is joined to the next by an edge.

• trail

• crawl

• run

• walk

A walk that involves no repeat use of edges and no repeat use of vertices.

• path

• bridge

• trail

• length

If I want to travel every edge once and I don't mind repeating vertices, I need to think...

• Bipartite graph

• Hamiltonian path

• Complete graph

• Eulerian trail

A path that starts and finishes at the same vertex.

• cycle

• trail

• closed walk

• loop

An edge that starts and finishes at the same vertex.

• node

• loop

• arc

• multiple edges

A graph/network that can be drawn without its edges crossing over.

• Graph theory

• Weighted graph

• Subgraph

• Planar graph

Any edge in a connected graph which, when removed, leaves the graph disconnected

• Path

• Bridge

• Trail

• Length

Two or more edges connecting the same two vertices

• Directed edges

• Adjacent edges

• Multiple edges

• Why do you do this to us?

A trail that starts and finishes at the same vertex

• Open trail

• Closed trail

• Semi trail

• No trail