Fig. 11

An illustration of combining two bi-rooted trees \(T_1=T_{\pmb {w}^1}\) and \(T_2=T_{\pmb {w}^2}\) with a new edge with multiplicity m joining vertices \(r_1(T_1)\) and \(r_1(T_2)\) to construct a target graph G, where \({\mathtt{a}}_i\in \Lambda \), \(d_i\in [1,d_\text {max}-1]\), \(m_i\in [d_i,{\text {val}}({\mathtt{a}}_i)-1]\), \(i = 1, 2\), and \(m \in [1, \min \{3, {\text {val}}({\mathtt{a}}_1) - m_1, {\text {val}}({\mathtt{a}}_2) - m_2\} ]\)