\$ ./flagmatic --r 2 --n 5 --induced-density 5:1223344551 --forbid 3.3 --dir output/c3maxc5 flagmatic version 1.5 ============================================================================ Optimizing for density of 5:1213243545. Forbidding 3.3 Using admissible graphs of order 5. Generated 1 type of order 1, with 5 flags of order 3. Generated 3 types of order 3, with [8, 6, 5] flags of order 4. Generated 14 admissible graphs. Approximate floating-point bound is 0.03840000 \$ sage -python scripts/find_sharp_graphs.py --dir output/c3maxc5 Floating point bound is 0.038400000791913261. 10 members of H are sharp. 0.038399999866059319 : graph 1 (5:) 0.038399999179418200 : graph 2 (5:12) 0.038400000469420784 : graph 3 (5:1213) 0.038400000146933733 : graph 5 (5:121314) 0.038400000630675675 : graph 8 (5:12131415) 0.038400000791913212 : graph 9 (5:12131425) 0.038399999824450450 : graph 10 (5:12132434) 0.038400000791913261 : graph 12 (5:1213142535) 0.038399999501926962 : graph 13 (5:1213243545) 0.038400000727425887 : graph 14 (5:121314253545) Written sharp graphs to flags.py \$ sage -python scripts/check_construction.py --n 5 --r 2 --induced-density 5:1223344551 --vertex-transitive 5:1223344551 Density of 5:1223344551 is 24/625. 10 graphs of order 5 occur as induced subgraphs of the blow-up: 5: has density 31/625 (0.049600) 5:12 has density 4/125 (0.032000) 5:1213 has density 12/125 (0.096000) 5:121314 has density 8/125 (0.064000) 5:12132434 has density 6/125 (0.048000) 5:12131425 has density 24/125 (0.192000) 5:12131415 has density 16/125 (0.128000) 5:1213243545 has density 24/625 (0.038400) 5:1213142535 has density 24/125 (0.192000) 5:121314253545 has density 4/25 (0.160000) \$ sage -python scripts/make_zero_eigenvectors.py --vertex-transitive 5:1223344551 --dir output/c3maxc5 Constructed 1 out of 1 zero eigenvectors for type 1. Constructed 4 out of 4 zero eigenvectors for type 2. Constructed 1 out of 1 zero eigenvectors for type 3. Constructed 2 out of 2 zero eigenvectors for type 4. Written zev.py Written field to flags.py \$ sage -python scripts/factor_approximate_q.py --dir output/c3maxc5 Floating point bound is 0.038400000791913261. Type 1: smallest eigenvalue is 0.020312545339158966 Type 2: smallest eigenvalue is 0.148959264212904008 Type 3: smallest eigenvalue is 0.176046112223611911 Type 4: smallest eigenvalue is 0.445612724880143529 Written r.py Written qdashf.py \$ sage -python scripts/make_exact_qdash.py '24/625' --denominator 90 --dir output/c3maxc5 --diagonalize Type 1: smallest eigenvalue is 0.033410999377025706 Type 2: smallest eigenvalue is 0.077272334886424918 Type 3: smallest eigenvalue is 0.137974605141859913 Type 4: smallest eigenvalue is 0.440783949073216219 Diagonalizing matrices... Written qdash.py Written r.py Added exact bound to flags.py \$ sage -python scripts/verify_bound.py --dir output/c3maxc5 Written q.py Floating point bound (non-sharp graphs) is 0.033600372704159928 Exact bound (just sharp graphs) is 24/625 Bound (all graphs) is 24/625 \$ sage -python scripts/make_certificate.py --dir output/c3maxc5 Written certificate to cert.js