Study of balance and symmetry of rooted trees

The Sacking index of a tree is a measure of balance which has beenintroduced in applications to phylogenetics. The study of this parameterin rooted binary trees, identifying its extremal values and enumerationof trees with given index, has been recently achieved by MareikeFischer. The goal of this project is to extend this analysis to particularly for the classes of rootedk-ary trees for general k. Finally, we will study the symmetry of the binary trees and we will propose some indexes to measure how symmetric is a tre