Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
graph
|
| gptkbp:application |
polyhedral graphs
|
| gptkbp:chromaticNumber |
3 or 4
2, 3, or 4 |
| gptkbp:defines |
A graph that is both planar and cubic (3-regular).
|
| gptkbp:degree |
3
|
| gptkbp:edgeCountFormula |
3n/2 (where n is the number of vertices)
|
| gptkbp:example |
Petersen graph (not planar)
cube graph tetrahedral graph |
| gptkbp:faceCountFormula |
f = n/2 + 2 (by Euler's formula)
|
| https://www.w3.org/2000/01/rdf-schema#label |
planar cubic graph
|
| gptkbp:isA |
gptkb:planar_graph
cubic graph |
| gptkbp:planarity |
planar
|
| gptkbp:property |
Every planar cubic graph can be embedded in the plane without edge crossings.
Every planar cubic graph is 3-edge-colorable except for snarks. |
| gptkbp:relatedTo |
gptkb:Four_color_theorem
gptkb:Euler's_formula polyhedra |
| gptkbp:vertexDegree |
3
|
| gptkbp:bfsParent |
gptkb:dodecahedron_graph
|
| gptkbp:bfsLayer |
6
|