GraphUtilities`
GraphUtilities`

MaximalIndependentVertexSet

As of Version 10, all the functionality of the GraphUtilities package is built into the Wolfram System. »

MaximalIndependentVertexSet[g]

gives a maximal independent vertex set of an undirected graph g.

MaximalIndependentVertexSet[g,w]

gives a maximal independent vertex set of g with vertices weighted by w.

Details and Options

• MaximalIndependentVertexSet functionality is now available in the built-in Wolfram Language function FindIndependentVertexSet.
• To use MaximalIndependentVertexSet, you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].
• MaximalIndependentVertexSet gives an (approximate) maximal set of vertices such that no two vertices form an edge. It treats the input as an undirected graph.
• The length of the vector w must be the same as the number of vertices in g.

Examples

Basic Examples(2)

This specifies a small graph:

This shows that the maximal independent vertex set contains three vertices:

MaximalIndependentVertexSet has been superseded by FindIndependentVertexSet:

Wolfram Research (2007), MaximalIndependentVertexSet, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/MaximalIndependentVertexSet.html.

Text

Wolfram Research (2007), MaximalIndependentVertexSet, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/MaximalIndependentVertexSet.html.

CMS

Wolfram Language. 2007. "MaximalIndependentVertexSet." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/GraphUtilities/ref/MaximalIndependentVertexSet.html.

APA

Wolfram Language. (2007). MaximalIndependentVertexSet. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/GraphUtilities/ref/MaximalIndependentVertexSet.html

BibTeX

@misc{reference.wolfram_2024_maximalindependentvertexset, author="Wolfram Research", title="{MaximalIndependentVertexSet}", year="2007", howpublished="\url{https://reference.wolfram.com/language/GraphUtilities/ref/MaximalIndependentVertexSet.html}", note=[Accessed: 09-September-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_maximalindependentvertexset, organization={Wolfram Research}, title={MaximalIndependentVertexSet}, year={2007}, url={https://reference.wolfram.com/language/GraphUtilities/ref/MaximalIndependentVertexSet.html}, note=[Accessed: 09-September-2024 ]}