# PlanarGraphQ

PlanarGraphQ[g]

yields True if g is a planar graph and False otherwise.

# Details

• A graph is planar if it can be drawn in the plane without edge crossings.

# Examples

open allclose all

## Basic Examples(2)

Test whether a graph is planar:

Not all graphs are planar:

## Scope(6)

PlanarGraphQ works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

PlanarGraphQ gives False for expressions that are not graphs:

PlanarGraphQ works with large graphs:

## Applications(2)

Four colors can be used to color a map with no two adjacent countries having the same color:

A color scheme:

Check whether non-overlapping utility lines can be used to distribute gas, water, and electricity:

## Properties & Relations(3)

Use GraphData for an extensive collection of planar graphs:

Non-planar graphs:

Use GraphLayout->"PlanarLayout" to lay out a planar graph:

For connected planar graphs with vertices and edges, with the number of faces:

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

#### Text

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

#### CMS

Wolfram Language. 2012. "PlanarGraphQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PlanarGraphQ.html.

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_planargraphq, author="Wolfram Research", title="{PlanarGraphQ}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/PlanarGraphQ.html}", note=[Accessed: 14-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_planargraphq, organization={Wolfram Research}, title={PlanarGraphQ}, year={2012}, url={https://reference.wolfram.com/language/ref/PlanarGraphQ.html}, note=[Accessed: 14-June-2024 ]}