Fig. 2
From: A multi-labeled tree dissimilarity measure for comparing “clonal trees” of tumor progression
a It shows how the set crucial vertices from Observation 2 changes after deleting a leaf u. We use dashed lines to denote correspondence among u and a vertex in a tree obtained by an edit operation. Only in the case (i), when a u was an unique child of p(u), u corresponds to p(u) in a tree after deletion of u. In other cases u does not correspond to any vertex in a new tree. In the case (ii) a vertex p(u) lost the status of a crucial in a tree after deletion and also does not correspond to the copy of himself in a new tree. In the case (iii) the vertex p(u) keep the status of a crucial and vertex and corresponds to the copy of himself. It is easy to see that the status of other vertices still unchanged and all vertices except p(u) corresponds to copies of himself in a new tree. b The figure illustrate changing a tree after expanding a vertex v into \(v_1\) and \(v_2\). We use dashed lines to denote correspondence between u in a tree before operation and a vertex in a new tree. In the case (i) v is non-crucial and both copies of v stays non-crucial. In the case (ii) a crucial vertex v corresponds to a crucial vertex \(v_2\)