Your job will be to write a function or a program, that will take an integer
n>0 as input and output a list of the edges of the
n-dimensional hypercube. In graph theory an edge is defined as a 2-tuple of vertices (or corners, if you prefer), that are connected.
A 1-dimensional hypercube is a line and features two vertices, which we will call
Therefore, the output will be:
The 4-dimensional hypercube (or tesseract) consists of 32 edges and its graph looks like this
and the output could look like this
[[a, b], [a, c], [a, e], [a, i], [b, d], [b, f], [b, j], [c, d], [c, g], [c, k], [d, h], [d, l], [e, f], [e, g], [e, m], [f, h], [f, n], [g, h], [g, o], [h, p], [i, j], [i, k], [i, m], [j, l], [j, n], [k, l], [k, o], [l, p], [m, n], [m, o], [n, p], [o, p]]
- You may name the vertices any way you like, as long as the name is unique.
- The edges are undirected, i.e.
[b, a]are considered the same edge.
- Your output must not contain duplicate edges.
- The output may be in any sensible format.
- Standard loopholes are forbidden.
Shortest code wins.