I have begun working with Mathematica for some Graph Theory, and I want to compute the number of spanning trees of all cubic graphs up to 12 vertices. I have found that
will give me the cubic graphs with 12 vertices. But how do I compute the number of spanning trees in each of these graphs. A good tutorial for Graph Theory with Mathematica seems impossible to find (I have found many, but none are actually readable). I can find this:
GraphData; Union[GraphData[#, "VertexCount"] & /@ %%]
to compute the number of vertices in all graphs on 8 vertices, but the #-tag is not defined, and &/@%% seems pretty magical.