# BooleanGraph

BooleanGraph[bfunc,g1,,gn]

gives the Boolean graph defined by the Boolean function bfunc on the graphs g1, , gn.

# Examples

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## Basic Examples(1)

The Boolean combination of two graphs:

## Scope(5)

BooleanGraph works with undirected graphs:

Directed graphs:

BooleanGraph works with as many graphs as the Boolean function:

Multigraphs:

Mixed graphs:

## Applications(4)

Define the symmetric graph difference Xor:

Convert the Boolean expression Xor to disjunctive normal form:

Implement it by related functions:

Compare to the result by using Xor directly:

Define the graph Nand:

Convert the Boolean expression Nand to disjunctive normal form:

Implement it by related functions:

Compare to the result by using Nand directly:

Define the graph Nor:

Convert the Boolean expression Nor to disjunctive normal form:

Implement it by related functions:

Compare to the result by using Nor directly:

Compute the Boolean graph for all Boolean functions of two variables:

Use BooleanFunction to enumerate all Boolean functions of two variables:

Compute the Boolean graph using these functions:

## Properties & Relations(3)

GraphUnion corresponds to Or:

GraphIntersection corresponds to And:

BooleanGraph does not necessarily produce simple graphs:

Use SimpleGraph if only a simple graph is needed:

Wolfram Research (2010), BooleanGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/BooleanGraph.html (updated 2014).

#### Text

Wolfram Research (2010), BooleanGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/BooleanGraph.html (updated 2014).

#### CMS

Wolfram Language. 2010. "BooleanGraph." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/BooleanGraph.html.

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_booleangraph, author="Wolfram Research", title="{BooleanGraph}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/BooleanGraph.html}", note=[Accessed: 15-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_booleangraph, organization={Wolfram Research}, title={BooleanGraph}, year={2014}, url={https://reference.wolfram.com/language/ref/BooleanGraph.html}, note=[Accessed: 15-July-2024 ]}