# pgRouting Manual (3.6)

## pgr_isPlanar - Experimental

# `pgr_isPlanar` - Experimental

`pgr_isPlanar` — Returns a boolean depending upon the planarity of the graph.

Boost Graph Inside

Warning

Possible server crash

- These functions might create a server crash

Warning

Experimental functions

- They are not officially of the current release.

- They likely will not be officially be part of the next release:

  - The functions might not make use of ANY-INTEGER and ANY-NUMERICAL

  - Name might change.

  - Signature might change.

  - Functionality might change.

  - pgTap tests might be missing.

  - Might need c/c++ coding.

  - May lack documentation.

  - Documentation if any might need to be rewritten.

  - Documentation examples might need to be automatically generated.

  - Might need a lot of feedback from the comunity.

  - Might depend on a proposed function of pgRouting

  - Might depend on a deprecated function of pgRouting

Availability

- Version 3.2.0

  - New experimental function

## Description

A graph is planar if it can be drawn in two-dimensional space with no two of its edges crossing. Such a drawing of a planar graph is called a plane drawing. Every planar graph also admits a straight-line drawing, which is a plane drawing where each edge is represented by a line segment. When a graph has \(K_5\) or \(K_{3, 3}\) as subgraph then the graph is not planar.

The main characteristics are:

- This implementation use the Boyer-Myrvold Planarity Testing.

- It will return a boolean value depending upon the planarity of the graph.

- Applicable only for undirected graphs.

- The algorithm does not considers traversal costs in the calculations.

- Running time: \(O(|V|)\)

## Signatures

Summary

pgr_isPlanar(Edges SQL)
RETURNS `BOOLEAN`

    SELECT * FROM pgr_isPlanar(
      'SELECT id, source, target, cost, reverse_cost
      FROM edges'
    );
     pgr_isplanar
    --------------
     t
    (1 row)

## Parameters

Parameter | Type | Description
--- | --- | ---
Edges SQL | `TEXT` | Edges SQL as described below.

## Inner Queries

### Edges SQL

Column | Type | Default | Description
--- | --- | --- | ---
`id` | ANY-INTEGER |  | Identifier of the edge.
`source` | ANY-INTEGER |  | Identifier of the first end point vertex of the edge.
`target` | ANY-INTEGER |  | Identifier of the second end point vertex of the edge.
`cost` | ANY-NUMERICAL |  | Weight of the edge (`source`, `target`)

`reverse_cost`

ANY-NUMERICAL

-1

Weight of the edge (`target`, `source`)

- When negative: edge (`target`, `source`) does not exist, therefore it’s not part of the graph.

Where:

ANY-INTEGER:

  `SMALLINT`, `INTEGER`, `BIGINT`

ANY-NUMERICAL:

  `SMALLINT`, `INTEGER`, `BIGINT`, `REAL`, `FLOAT`

## Result columns

Returns a boolean `(pgr_isplanar)`

Column | Type | Description
--- | --- | ---

`pgr_isplanar`

`BOOLEAN`

- true when the graph is planar.

- false when the graph is not planar.

## Additional Examples

The following edges will make the subgraph with vertices {10, 15, 11, 16, 13} a \(K_1\) graph.

    INSERT INTO edges (source, target, cost, reverse_cost) VALUES
      (10, 16, 1, 1), (10, 13, 1, 1),
      (15, 11, 1, 1), (15, 13, 1, 1),
      (11, 13, 1, 1), (16, 13, 1, 1);
    INSERT 0 6

The new graph is not planar because it has a \(K_5\) subgraph. Edges in blue represent \(K_5\) subgraph.

    SELECT * FROM pgr_isPlanar(
      'SELECT id, source, target, cost, reverse_cost
      FROM edges');
     pgr_isplanar
    --------------
     f
    (1 row)

## See Also

- Sample Data

- https://www.boost.org/libs/graph/doc/boyer_myrvold.html

Indices and tables

- Index

- Search Page