The solution to the number of spanning trees of the graph below is given by $3 \times 2 \times 3 = 18$. I'm not sure how to get this. Please assist. Thanks!

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Notes: Just in case anyone was wondering, I drew the graph using the tool on http://illuminations.nctm.org/Activity.aspx?id=3550 and got the image by using the snipping tool on Windows.


1 Answer 1


Any spanning tree in the graph must contain exactly one CD edge, and this edge can be chosen in two ways. For the subgraph to be connected, C must be in the same component as A and B. Thus two of the three edges in the triangle ABC need to be included, and these two edges can be chosen in 3 ways. Similarly the two edges in the triangle CEF can be chosen in 3 ways. Thus the number of spanning trees is $2 \times 3 \times 3 =18$.


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