nonseparable graph

A biconnected graph is a connected graph having no articulation vertices. An equivalent definition for graphs on more than two vertices is a graph G having vertex connectivity κ(G)>=2. The numbers of biconnected simple graphs on n = 1, 2, ... nodes are 0, 0, 1, 3, 10, 56, 468, ... (cf. OEIS A002218). The first few of these are illustrated above. Maximal connected graphs on two or more vertices are called blocks or nonseparable graphs. Biconnected graphs are closely related to blocks. If a block has more than two vertices, then it is biconnected. Conversely, biconnected graphs on two or more vertices are blocks.

articulation vertex | block | connected graph | k-connected graph