Chapter 5: Euler Paths and Circuits

Connected graph

A graph such that there is a path going from any vertex to any other vertex

Disconnected graph

A graph that is not connected, it has two or more connected components

Simple graph

A graph with no loops or multiple edges

Euler path

A path that travels along each edge of a graph once and only once

Path

A sequence of edges each adjacent to the next, with no edge included more than once, and starting and ending at different vertices

Clique

A set of vertices with the property that any two are adjacent

Isolated vertex

A vertex of one degree

Bridges

An edge in a connected graph without which the graph would be disconnected

Loop

An edge that connects a vertex with itself

Circuit

Same as a path but starting and ending at the same vertex

Euler circuit

A circuit that travels along each edge of a graph once and only once

Length

Number of edges in a path or a circuit

Degree

Number of edges meeting at the vertex

Adjacent edges

Two edges with a shared vertex

Multiple edges

Two or more edges connecting the same two vertices

Adjacent vertices

Two vertices connected by an edge

Components

the connected "pieces" that make up a graph