Connected components and cuts in undirected graphs
A graph which is not connected is the union of two or more connected
subgraphs, each pair of which has no vertex in common. These disjoint
connected subgraphs are called the connected components of the graph.
A vertex is called a cut vertex, if its removal, together with the removal
of all the edges incident with it, produces a subgraph with more
connected components than in the original graph.
The removal of a cut vertex or cut edge from a connected graph
Similarly, an edge whose removal produces a graph with more connected
components than in the original graph, is called a cut edge or bridge.