# FindGraphIsomorphism

FindGraphIsomorphism[g1,g2]

finds an isomorphism that maps the graph g1 to g2 by renaming vertices.

FindGraphIsomorphism[g1,g2,n]

finds at most n isomorphisms.

FindGraphIsomorphism[{vw,},]

uses rules vw to specify the graph g.

# Examples

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## Basic Examples(2)

Find an isomorphism that maps two graphs:

Find all isomorphisms:

## Scope(8)

### Specification(5)

FindGraphIsomorphism works with undirected graphs:

Directed graphs:

Use rules to specify the graph:

It returns an empty list if no isomorphism can be found:

FindGraphIsomorphism works with large graphs:

### Enumeration(3)

Find an isomorphism that maps two graphs:

Find at most two isomorphisms:

Find all isomorphisms:

## Applications(1)

Find an isomorphism that maps two graphs:

Highlight and label two graphs according to the mapping:

## Properties & Relations(3)

Isomorphic graphs have the same number of vertices and edges:

Test whether two graphs are isomorphic using IsomorphicGraphQ:

Isomorphic graphs have the same canonical graph:

Wolfram Research (2010), FindGraphIsomorphism, Wolfram Language function, https://reference.wolfram.com/language/ref/FindGraphIsomorphism.html (updated 2015).

#### Text

Wolfram Research (2010), FindGraphIsomorphism, Wolfram Language function, https://reference.wolfram.com/language/ref/FindGraphIsomorphism.html (updated 2015).

#### CMS

Wolfram Language. 2010. "FindGraphIsomorphism." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/FindGraphIsomorphism.html.

#### APA

Wolfram Language. (2010). FindGraphIsomorphism. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindGraphIsomorphism.html

#### BibTeX

@misc{reference.wolfram_2023_findgraphisomorphism, author="Wolfram Research", title="{FindGraphIsomorphism}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/FindGraphIsomorphism.html}", note=[Accessed: 28-September-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2023_findgraphisomorphism, organization={Wolfram Research}, title={FindGraphIsomorphism}, year={2015}, url={https://reference.wolfram.com/language/ref/FindGraphIsomorphism.html}, note=[Accessed: 28-September-2023 ]}