Table 4.

Illustration of digraph f in Figure 2.

$n$	$n=0$	$n=1$	$n=2$
${\Omega }_n$	$\text{span}\left\{e_1,e_2,e_3,e_4,e_5,e_6\right\}$	$\text{span}\left\{e_{12},e_{15},e_{23},e_{26},e_{42},e_{45},e_{53},e_{56}\right\}$	$\text{span}\{e_{153}-e_{123},e_{156}-e_{126},e_{453}-e_{423},e_{456}-e_{426}\}$
$B_{n+1}$	$\begin{array}{c}\\ e_1\\ e_2\\ e_3\\ e_4\\ e_5\\ e_6\end{array}\begin{array}{c}\begin{array}{cccccccc}{e}_{12}& e_{15}& e_{23}& e_{26}& e_{42}& e_{45}& e_{53}& e_{56}\end{array}\\ \left(\begin{array}{cccccccc}-1& -1& 0& 0& 0& 0& 0& 0\\ 1& 0& -1& -1& 1& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& -1& -1& 0& 0\\ 0& 1& 0& 0& 0& 1& -1& -1\\ 0& 0& 0& 1& 0& 0& 0& 1\end{array}\right)\end{array}$	$\begin{array}{c}\\ e_{12}\\ e_{15}\\ e_{23}\\ e_{26}\\ e_{42}\\ e_{45}\\ e_{53}\\ e_{56}\end{array}\begin{array}{c}\begin{array}{cccc}{e}_{153}-e_{123}& e_{156}-e_{126}& e_{453}-e_{423}& e_{456}-e_{426}\end{array}\\ \left(\begin{array}{cccc}-1& -1& 0& 0\\ 1& 1& 0& 0\\ -1& 0& -1& 0\\ 0& -1& 0& -1\\ 0& 0& -1& -1\\ 0& 0& 1& 1\\ 1& 0& 1& 0\\ 0& 1& 0& 1\end{array}\right)\end{array}$	$4\times 0$ empty matrix
$L_n$	$\left(\begin{array}{cccccc}2& -1& 0& 0& -1& 0\\ -1& 4& -1& -1& 0& -1\\ 0& -1& 2& 0& -1& 0\\ 0& -1& 0& 2& -1& 0\\ -1& 0& -1& -1& 4& -1\\ 0& -1& 0& 0& -1& 2\end{array}\right)$	$\left(\begin{array}{cccccccc}4& -1& 0& 0& 1& 0& -1& -1\\ -1& 4& -1& -1& 0& 1& 0& 0\\ 0& -1& 4& 1& 0& -1& -1& 0\\ 0& -1& 1& 4& 0& -1& 0& -1\\ 1& 0& 0& 0& 4& -1& -1& -1\\ 0& 1& -1& -1& -1& 4& 0& 0\\ -1& 0& -1& 0& -1& 0& 4& 1\\ -1& 0& 0& -1& -1& 0& 1& 4\end{array}\right)$	$\left(\begin{array}{cccc}4& 2& 2& 0\\ 2& 4& 0& 2\\ 2& 0& 4& 2\\ 0& 2& 2& 4\end{array}\right)$
${\beta }_n$	1	0	1
$\text{Spectra}\left(L_n\right)$	{0, 2, 2, 2, 4, 6}	{2, 2, 2, 4, 4, 4, 6, 8}	{0, 4, 4, 8}