Unrooted binary tree: Difference between revisions

Revision as of 02:22, 5 April 2022

Revision as of 07:20, 6 May 2023

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* <math> p_{i,i}=0 </math> for all <math> i\in [1,n]</math>

* <math> p_{i,j}=p_{j,i} </math> for all <math> i,j\in [1,n]: i\neq j</math>

* <math> p_{i,ij}\leq p_{i,k} + p_{k,j} </math> for all <math> i,j,k\in [1,n]: i\neq j\neq k</math>

* <math> \sum_{j=1}^{n} 1/2^{p_{i,j}}=1/2 </math> for all <math> i\in [1,n]</math> (which is an adaptation of the [[Kraft–McMillan inequality]])

* <math> \sum_{i=1}^n\sum_{j=1}^{n} p_{i,j}/2^{p_{i,j}}=2n-3 </math>, also referred to as the ''phylogenetic manifold''.<ref name="On the Balanced Minimum Evolution P"/>