vertices(LeafTree) -- list the vertices of a tree

Synopsis

Function: vertices
Usage:

vertices T
Inputs:
- T, an instance of the type LeafTree,
Outputs:
- a list, the vertices of T

Description

This function lists all vertices of a tree. Each vertex is specified by the partition of the set of leaves formed by removing the vertex. Each partition is given as a list of sets.

i1 : T = leafTree(4,{{0,1}});

i2 : vertices T

o2 = {set {set {0, 1}, set {2}, set {3}}, set {set {0, 1, 2}}, set {set {0,
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     1, 3}}, set {set {0}, set {1}, set {2, 3}}, set {set {0, 2, 3}}, set
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     {set {1, 2, 3}}}

o2 : List

i3 : #(vertices T)

o3 = 6

Caveat

The leaves of T in the output of vertices have a different representation from the one in the output of leaves(LeafTree).

Ways to use this method: