Suppose $G = (V, A)$ is the acyclic weakly connected digraph with$ V $consisting of vertices $v_{i}$ $(i = 1, 2, ..., 8)$ in which the seven arcs are $(v 1 , v 2 ), (v 3 , v 2 ), (v 4 , v 3 ),(v 7 , v 2 ),( v 3 , v 6 ), (v 5 , v 6 )$ and $(v 8 , v 7 )$. Relabel the vertices and arcs such that when the last row of the incidence matrix is deleted, the truncated matrix is upper triangular and non-singular.
Aunt Google does not tell me what is relabel and why we need relabel. Could any one use this example to explain why we need relabel and how to relabel?