Fig. 5

An illustration of selecting a subgraph H from the scheme graph \(\text {SG}( d_\text {max}, k^*, \text {bh}^*, t^*=n^*-{\text {bl}}^*-1)\): a An acyclic graph \(H\in {\mathcal {H}}(n^*, d_\text {max}, \text {dia}^*, k^*, \text {bh}^*, {\text {bl}}^*)\) with \(n^*=37\), \(d_\text {max}=3\), \(\text {dia}^*(H)=17\), \(k^*=2\), \(\text {bh}^*=2\) and \({\text {bl}}^*=3\), where the labels of some vertices indicate the corresponding vertices in the scheme graph \(\text {SG}( d_\text {max}, k^*, \text {bh}^*, t^*)\); b The \(k^*\)-branch-tree of H for \(k^*=2\); c An acyclic graph \(H'\) selected from \(\text {SG}( d_\text {max}, k^*, \text {bh}^*, t^*)\) as a graph that is isomorphic to H in (a)