KVertexConnectedComponents

KVertexConnectedComponents[g, k] gives the k-vertex-connected components of the graph g.

KVertexConnectedComponents[g, k, {v1, v2, ...}] gives the k-vertex-connected components that include at least one of the vertices v1, v2, ….

Examples

KVertexConnectedComponents[PetersenGraph[], 2]

KVertexConnectedComponents[CompleteGraph[5], 3]

Please visit the official Wolfram Language Reference for more details.