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A tree is a connected graph without cycles, with a finite or infinite number of vertices. There are many variants of trees, according to further constraints or decorations.

9 votes
3 answers
13k views

Number of trees with n nodes and m leaves

Even searching for " 'number of trees' leaves " didn't reveal what I am looking for: an approach for calculating the (approximate) number of trees with exactly n nodes and m leaves. …
4 votes
1 answer
222 views

A distinguishing node property in trees?

Consider a tree with k nodes and for each node v the vector lv = (lv0, lv1, ..., lvk-1) with lvd the number of leaves (!) with distance d to v. I wonder whether two nodes v, w with lv = lw are conjuga …