Macaulay2 » Documentation
Packages » Matroids :: wheel
next | previous | forward | backward | up | index | toc

# wheel -- wheels/whirls

- Usage:
    `M = wheel r`
    `M = whirl r`
- Inputs:
  - r, an integer,
- Outputs:
  - a matroid, a rank r wheel or whirl

## Description

The families of wheels and whirls appears in Oxley, p. 659-660. The rank-r wheel is the graphic matroid of the wheel graph with r outer vertices, and has 2r elements. The rank-r whirl is the unique relaxation of the rank-r wheel (and thus also has 2r elements).

    i1 : M = wheel 3

    o1 = a "matroid" of rank 3 on 6 elements

    o1 : Matroid

    i2 : M == matroid wheelGraph 4

    o2 = true

    i3 : N = whirl 3

    o3 = a "matroid" of rank 3 on 6 elements

    o3 : Matroid

    i4 : areIsomorphic(N, relaxation M)

    o4 = true

## See also

- wheelGraph -- Constructs a wheel graph
- specificMatroid -- creates built-in matroid

## Ways to use wheel:

- `wheel(ZZ)`

## For the programmer

The object wheel is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Matroids/doc-Matroids.m2:3319:0.