Hey guys I'm try to count the number of trees with number of vertices = n,
such that all vertices except for two have degree 2.
I would like to get some hint for that question , thank you!
2026-03-29 05:34:27.1774762467
Counting trees with condition
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Since the total number of edges in a trees with $n$ vertices is $n\!-\!1$, and the sum of vertex degrees is twice the number of edges, we can see that the two vertices with degree $\ne 2$ both have degree $1$. There is therefore only one such tree for each value of $n$ - a path.