Use the command graphs.CubeGraph(4) to build the four-dimensional cube graph, Q4. Using a plain .plot() command (without a spring layout) should create a nice plot. Construct the automorphism group of the graph, which will provide a group action on the vertex set.
(a) Construct the orbits of this action, and comment.
(b) Construct a stabilizer of a single vertex (which is a subgroup of the full automorphism group) and then consider the action of this group on the vertex set. Construct the orbits of this new action, and comment carefully and fully on your observations, especially in terms of the vertices of the graph.