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Section3.4Cubelike Graphs

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

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.

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.