Rooted vs. Unrooted Phylogenetic trees diversity

Tree Counts Unrooted binary trees 4 taxa → 3 distinct trees A tree with n taxa has n-2 inner nodes And 2n-3 branches Rooted binary trees 4 taxa → 3 unrooted trees * 5 branches each (rooting points) = 15 trees n-1 inner nodes 2n-2 branches The number of rooted trees for n taxa simply is the number of unrooted trees for n+1 taxa The additional (n+1th) taxon represents all possible rootings for the # of unrooted trees with n taxa