For any n: find n non-isomorphic trees, that have the same degree sequences!

(n is a natural number)

I guess we should find an algorithm (input: n, output: n suitable trees).

What if we create a 2n+1 long chain and we can connact another vertex to n places in order to have n non-ismorphic trees with the same degree sequences.

I am afraid this algoritm doesn't work for all n or there is a mistake in my come-off.

Any help would be appreciated!