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Problem: Trying to come up with a systematic approach to listing non-pairwise isomorphic spanning trees of $Q_3$ the

$k$-cube graph of size 3.

Thoughts

Constructing two sets say $X,Y$ as a bipartite partition where

$X = \{ 000, 011, 101, 110 \}$ $Y = \{ 001, 010, 001, 111 \}$. Then I want to list them in some methodical way but I am not sure how to begin without drawing endless pictures.

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    One approach might be to think about degree sequences here. There are spanning paths (no branching) and some spanning trees with a couple nodes of degree 3; perhaps you could try and enumerate trees with 8 nodes and with degrees between 1 and 3. I would imagine they don't *all* correspond to spanning trees of the cube, but I would hope there aren't too many of these, and it might not be too hard to decide which are subgraphs of the cube graph. – 2017-02-09

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