Vertices of a LeafTree do not have explicit names. Therefore a vertex v is specified by naming an edge e incident to v, and leaf l on the opposite side of the edge as v.
The function outputs the subtrees of T obtained by deleting the vertex v from T and then re-adding v to each of the resulting subtrees as a new leaf. The new leaf on each subtree is adjacent to the edge previously adjacent to v on T. Each subtree has a copy of the vertex labeled newl, but their edge sets are disjoint.
Each subtree in P may have at most one leaf that was not a leaf of T, and therefore previously unlabeled. This leaf label is determined by the user and input as newl.
i1 : T = leafTree(4,{{0,1}})
o1 = {{0, 1, 2, 3}, {set {0, 1}, set {0}, set {1}, set {2}, set {3}}}
o1 : LeafTree
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i2 : P = vertexCut(T, set {0,1}, 0, 4);
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i3 : P#0
o3 = {{3, 4}, {set {3}}}
o3 : LeafTree
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i4 : P#1
o4 = {{2, 4}, {set {2}}}
o4 : LeafTree
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i5 : P#2
o5 = {{0, 1, 4}, {set {0}, set {1}, set {4}}}
o5 : LeafTree
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