A cubelike graph is a Cayley graph for $\ints_2^d$. The connection
set of such a graph can be encoded by a $d\times m$ matrix with distinct
columns. If $M$ is such a matrix then we can get a list of its columns with `cols = M.columns()`

and we can recover $M$ with `M = Matrix(cols).transpose()`

.

The natural choice for the vertices of a cubelike graph are the elements of

V = VectorSpace( GF(2)), d) # not tested

but these are not hashable. We can make a vector `v`

hashable with `v.set_immutable()`

and use vectors as vertices, or work as follows. Suppose that `vls`

is a list of vectors from a vector space `V`

.

G = Graph( [[0..len(vls)-1],\ lambda i,j: vls[i]-vls[j] in V.list()]) # not tested

P = graphs.PetersenGraph() D = P.incidence_matrix() B = D.change_ring( GF(2)) # convert to a matrix over GF(2) B0 = B.submatrix( nrows=B.nrows()-1) # delete last row B0

[1 1 1 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 1 1 1 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 1 1 1 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 1 1 1 0 0 0 0 0 0] [0 1 0 0 0 0 0 0 1 1 0 0 0 0 0] [1 0 0 0 0 0 0 0 0 0 1 1 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0 1 1 0] [0 0 0 0 0 1 0 0 0 0 0 1 0 0 1] [0 0 0 0 0 0 0 1 0 0 1 0 0 1 0]

For humans it can be convenient to encode binary vectors of length $d$ as integers between 0 and $2^{d-1}$. With $G$ as just defined, its connection set will be the correct set of integers.

def cubelike(vecls): d = len(vecls[0]) VS = VectorSpace(GF(2),d) return Graph([[0..(2^d-1)], lambda i,j: VS[i]-VS[j] in vecls])

PP = cubelike(B0.columns()) PP.am().fcp()

(x - 15) * (x + 9)^5 * (x - 9)^10 * (x - 7)^15 * (x + 7)^30 * (x - 5)^36 * (x + 3)^60 * (x + 5)^60 * (x + 1)^75 * (x - 3)^100 * (x - 1)^120