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