OFFSET
0,11
COMMENTS
T(n,k) is the number of graphs on n nodes with incidence matrix of rank n-k, where the incidence matrix is defined as in Godsil-Royle reference below.
REFERENCES
C. Godsil and G. Royle, Algebraic Graph Theory, Springer, 2001, page 166.
EXAMPLE
Triangle T(n,k) begins:
1;
0, 1;
0, 1, 1;
1, 1, 1, 1;
3, 4, 2, 1, 1;
16, 9, 5, 2, 1, 1;
96, 37, 13, 6, 2, 1, 1;
812, 162, 46, 14, 6, 2, 1, 1;
...
MATHEMATICA
Needs["Combinatorica`"];
Table[Table[Count[Prepend[Flatten[Table[g = {n, k}; b = GraphData[g, "IncidenceMatrix"]; {n - MatrixRank[b]}, {k, 2, NumberOfGraphs[n]}]], n], i], {i, 0, n}], {n, 0, 7}] // Grid
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Mar 04 2020
STATUS
approved