Question

For unrooted trees, the number of unrooted tree topologies (NU) is ________

(a) NU = (2n− 5)!/2^n−3(n− 5)!

(b) NU = (2n− 5)!/2^n−3(n− 3)!

(c) NU = (2n− 5)!/2^−2(n− 3)!

(d) NU = (2n− 5)!/2^n(n− 3)!

The question was posed to me in my homework.

My doubt stems from Forms of Tree Representation in section Molecular Phylogenetics of Bioinformatics

Answer 1

Correct option is (b) NU = (2n− 5)!/2^n−3(n− 3)!

Explanation: The number of possible topologies increases extremely rapidly with the number of taxa. For six taxa, there are 105 unrooted trees and 945 rooted trees. If there are ten taxa, there can be 2,027,025 unrooted trees and 34,459,425 rooted ones.