# FindVertexCut

finds a smallest vertex cut of the graph g.

FindVertexCut[g,s,t]

finds a smallest s-t vertex cut of the graph g.

FindVertexCut[{vw,},]

uses rules vw to specify the graph g.

# Details

• A vertex cut is also known as vertex cut set or separating set.
• A vertex cut of a graph g is a list of vertices whose deletion from g disconnects g.
• The s-t vertex cut is a list of vertices whose deletion from g disconnects g, with s and t in two different connected components.
• For a disconnected graph, FindVertexCut will return an empty list {}.

# Examples

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## Basic Examples(2)

Find a smallest vertex cut:

Highlight a vertex cut:

Find a smallest vertex cut between two vertices:

## Scope(6)

FindVertexCut works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Find a smallest s-t vertex cut:

Use rules to specify the graph:

## Properties & Relations(1)

Use VertexConnectivity to obtain the size of the vertex cut:

Wolfram Research (2012), FindVertexCut, Wolfram Language function, https://reference.wolfram.com/language/ref/FindVertexCut.html (updated 2015).

#### Text

Wolfram Research (2012), FindVertexCut, Wolfram Language function, https://reference.wolfram.com/language/ref/FindVertexCut.html (updated 2015).

#### CMS

Wolfram Language. 2012. "FindVertexCut." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/FindVertexCut.html.

#### APA

Wolfram Language. (2012). FindVertexCut. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindVertexCut.html

#### BibTeX

@misc{reference.wolfram_2024_findvertexcut, author="Wolfram Research", title="{FindVertexCut}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/FindVertexCut.html}", note=[Accessed: 24-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_findvertexcut, organization={Wolfram Research}, title={FindVertexCut}, year={2015}, url={https://reference.wolfram.com/language/ref/FindVertexCut.html}, note=[Accessed: 24-July-2024 ]}