Fig. 6

Network N^u (adapted from [5]) and the set \( \mathcal{LCON}\left({N}^u\right) \) resulting from the leaf connecting procedure. G₁ is obtained by deleting leaves 1,2 and 3,4 and connecting their attachment points respectively, while G₂ is obtained by connecting leaves 1,3 and 2,4 and G₃ is obtained by connecting leaves 1,4 and 2,3. Note that in case of G₁, 4 vertices (a,b,a’,b’) have to be introduced in order to prevent the graph from becoming a multigraph. For G₂ and G₃ this step is not necessary. Note, however, in any case the number of vertices of a graph in \( \mathcal{LCON}\left({N}^u\right) \) cannot increase compared to N^u, because in each step 2 leaves are deleted and at most 2 new vertices are created