$ ./flagmatic --r 3 --n 6 --forbid-k4 --forbid-induced 4.1 --dir output/k441
flagmatic version 1.5
============================================================================
Forbidding 4.4
Forbidding 4.1 as an induced subgraph.
Using admissible graphs of order 6.
Generated 1 type of order 0, with 2 flags of order 3.
Generated 1 type of order 2, with 8 flags of order 4.
Generated 3 types of order 4, with [15, 15, 17] flags of order 5.
Generated 34 admissible graphs.
Approximate floating-point bound is 0.55555556

$ sage -python scripts/find_sharp_graphs.py --dir output/k441
Floating point bound is 0.555555557483315088.
8 members of H are sharp.
0.555555554189191003 : graph 1 (6:)
0.555555556177857124 : graph 2 (6:123124125126)
0.555555556613102297 : graph 10 (6:123124125136146156236246256)
0.555555557193247784 : graph 11 (6:123124125126134135136145146156)
0.555555557483226936 : graph 23 (6:123124125126134135136145146256356456)
0.555555556178151999 : graph 26 (6:123124125134135145236246256346356456)
0.555555557483315088 : graph 31 (6:123124125126134135136245246256345346356)
0.555555557048232007 : graph 34 (6:123124125134135146156236245246256345346356)
Written sharp graphs to flags.py

$ sage -python scripts/check_construction.py --n 6 --r 3 --vertex-transitive 3:123112223331
Density is 5/9.
8 graphs of order 6 occur as induced subgraphs of the blow-up:
6: has density 7/243 (0.028807)
6:123124125126 has density 5/81 (0.061728)
6:123124125136146156236246256 has density 20/243 (0.082305)
6:123124125126134135136145146156 has density 4/27 (0.148148)
6:123124125134135145236246256346356456 has density 5/81 (0.061728)
6:123124125126134135136145146256356456 has density 20/81 (0.246914)
6:123124125126134135136245246256345346356 has density 20/81 (0.246914)
6:123124125134135146156236245246256345346356 has density 10/81 (0.123457)

$ sage -python scripts/make_zero_eigenvectors.py --vertex-transitive 3:123112223331 --dir output/k441
Constructed 1 out of 1 zero eigenvectors for type 1.
Constructed 3 out of 3 zero eigenvectors for type 2.
Constructed 5 out of 5 zero eigenvectors for type 3.
Constructed 1 out of 1 zero eigenvectors for type 4.
Constructed 4 out of 4 zero eigenvectors for type 5.
Written zev.py
Written field to flags.py

$ sage -python scripts/factor_approximate_q.py --dir output/k441
Floating point bound is 0.555555557483314866.
Type 1: smallest eigenvalue is 0.180758628947732980
Type 2: smallest eigenvalue is 0.025204209832725446
Type 3: smallest eigenvalue is 0.127913863682220269
Type 4: smallest eigenvalue is 0.116791535663077511
Type 5: smallest eigenvalue is 0.099219286066487625
Written r.py
Written qdashf.py

$ sage -python scripts/make_exact_qdash.py '5/9' --denominator 20 --dir output/k441 --diagonalize
Type 1: smallest eigenvalue is 0.185903308023694175
Type 2: smallest eigenvalue is 0.042807554280651042
Type 3: smallest eigenvalue is 0.119609206380504790
Type 4: smallest eigenvalue is 0.115233084293317356
Type 5: smallest eigenvalue is 0.101916830401031111
Diagonalizing matrices...
Written qdash.py
Written r.py
Added exact bound to flags.py

$ sage -python scripts/verify_bound.py --dir output/k441
Written q.py
Floating point bound (non-sharp graphs) is 0.555366999334846678
Exact bound (just sharp graphs) is 5/9
Bound (all graphs) is 5/9

$ sage -python scripts/make_certificate.py --dir output/k441
Written certificate to cert.js