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# vertexCuts -- lists all the vertex cuts of a graph

- Usage:
    `C = vertexCuts G`
- Inputs:
  - G, a graph,
- Outputs:
  - C, a list, the list of vertex cuts of a graph

## Description

A vertex cut is a set of vertices that, when removed from a graph, make the graph have more than one component. The complete graph has no vertex cuts, so the method returns an empty list.

    i1 : G = cycleGraph 5;

    i2 : vertexCuts G

    o2 = {{0, 2}, {0, 3}, {1, 3}, {0, 1, 3}, {0, 2, 3}, {1, 4}, {2, 4}, {0, 2,
         ------------------------------------------------------------------------
         4}, {1, 2, 4}, {1, 3, 4}}

    o2 : List

## See also

- minimalVertexCuts -- finds the minimal vertex cuts of a graph
- vertexConnectivity -- computes the vertex connectivity of a graph
- edgeCuts -- returns the edge cuts of a graph

## Ways to use vertexCuts:

- `vertexCuts(Graph)`

## For the programmer

The object vertexCuts is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Graphs.m2:3012:0.