In a certain exercise I am given a graph consisting of three triangles united by one central vertex, having a total of 8 vertex and 9 edges. I am asked to find the number of spanning trees. It seems really easy and I find it weird to be something so simple, that's why I prefer asking here in order to assure the exactitude of my answer. Here is my attempt:
In order to form a tree, all edges than can create a cycle have to dissapear, but since I am looking for spanning trees, all vertex have to be connected. Therefore, for each triangle, one just can remove one edge, having three options for each triangle. Therefore, there are $3^3 = 27$ options. Is this as simple as that?
2026-03-30 00:21:16.1774830076
Number of spanning trees of a special graph
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