How many minimum spanning tree of following graph is possible.
My attempt:
I've tried it manually as :
Therefore,
Total possible number of minimum spanning trees are $=2\times2\times2+2\times2+2=8+4+2=14$
Can you explain in formal way, please?
2026-04-01 00:45:33.1775004333
How many minimum spanning tree of following graph is possible.
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We can remove the edge of weight $7$, since it could be replaced by the other edges of the rectangle, whose weights add to $6$. The resulting graph has $3$ cut vertices, and all minimal spanning trees in the $4$ components they separate can be arbitrarily combined. From left to right, there are $3$, $1$, $3$ and $2$ minimal spanning trees for the components, for a total of $3\cdot1\cdot3\cdot2=18$. (You were missing $4$ trees from the case where you would have had "$2$ options" in the first component and the two diagonal edges in the third component.)