Prove that a graph cannot have EXACTLY two distinct spanning trees.
2026-03-30 12:19:35.1774873175
Prove graph cannot have exactly two distinct spanning trees
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I assume you mean simple graphs, not true for multi-graphs.
The union of the two spanning trees contains a cycle (contains too many edges to be a tree), cycles have length greater than $2$. Removing any edge from a cycle leaves a connected graph, so the union of the two spanning trees has at least $3$ spanning trees, each of which is a spanning tree for the original graph.