The entry $N_{ij}$ is the number of induced subgraphs of $\Lambda_i$ that are isomorphic to $\Lambda_j$. It is a lower triangular matrix with diagonal entries 1. The computation of the chromatic polynomial is performed by a recursive procedure beginning with the first row of the $\mathcal{N}$-matrix, computing at each step certain polynomials in terms of the corresponding polynomials for non-quasi-separable induced subgraphs on fewer vertices. A few observations about the procedure are useful to motivate the work in this paper. The graphs $C_4$ and $K_4$ are the only non-quasi-separable graphs on $4$ vertices. Also, for any $i$, $N_{i1}=v(\Lambda_i)$, and $N_{i2}= e(\Lambda_i)$. Therefore, graphs on 4 or fewer vertices that index the first few rows of the $\mathcal{N}$-matrix can be inferred from the matrix entries. Therefore, we conclude that the computation of the chromatic polynomial can be performed on the matrix entries alone, even if the induced subgraphs indexing the rows and the columns of $\mathcal{N}(G)$ are unspecified. Therefore, we will think of the $\mathcal{N}$-matrix as [*unlabelled* ]{}, that is, we will assume that the induced subgraphs indexing the rows and the columns are not given.

A natural question is what other invariants can be computed from the (unlabelled) $\mathcal{N}$-matrix? Obviously, 