PetersenGraph

The Petersen graph — the standard 10-vertex, 15-edge, 3-regular example graph.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguagePetersenGraph✓↗

PetersenGraph()outer 5-cycle (vertices 1-5), inner pentagram (6-10, step 2), and the 5 spokes joining $i$ to $i + 5$.

Typed signatures

Type	Package	Applies
() -> value	combinatorics	always

Domain: Collections

Details

• 3-regular, non-bipartite (girth 5, so it has odd cycles), and connected — every property a reader would reach for this graph to demonstrate.

Examples

2 more kept as data, checked against the oracles

Basic #

Every vertex has degree 3

live ↗

In$\mathrm{VertexDegree}(\mathrm{PetersenGraph}())$Out$\bigl\lbrack3, 3, 3, 3, 3, 3, 3, 3, 3, 3\bigr\rbrack$

Its girth is 5 (odd), so it is not bipartite

live ↗

In$\mathrm{IsBipartiteGraph}(\mathrm{PetersenGraph}())$Out$\mathrm{False}$

About

Examples	4
Checked against	Wolfram Language 4 agree
Crosswalk	Wolfram Language

See also: CycleGraph, IsBipartiteGraph