& 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
2 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\
3 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\
3 & 2 & 2 & 0 & 1 & 0 & 0 & 0 & 0 \\
4 & 1 & 2 & 1 & 0 & 1 & 0 & 0 & 0 \\
4 & 0 & 4 & 0 & 0 & 0 & 1 & 0 & 0 \\
6 & 3 & 6 & 1 & 2 & 2 & 1 & 1 & 0 \\
9 & 6 & 12 & 2 & 6 & 6 & 3 & 6 & 1 \\
\end{pmatrix}$$

Let us associate an [*edge labelled poset*]{} with the graph $G$. Define a partial order $\preceq $ on the set $\Lambda(G)$ as follows: $\Lambda_j \preceq \Lambda_k$ if and only if $\Lambda_j$ is an induced subgraph of $\Lambda_k$. This poset is 