loaded graph dc1024
loaded graph dc2048
loaded graph properties data file
loaded graph invariants data file
independence_number(x) >= average_distance(x)
independence_number(x) >= radius(x)
independence_number(x) >= residue(x)
independence_number(x) >= max_even_minus_even_horizontal(x)
independence_number(x) >= critical_independence_number(x)
independence_number(x) >= max_degree(x) - number_of_triangles(x)
independence_number(x) >= -average_distance(x) + ceil(lovasz_theta(x))
independence_number(x) >= min_degree(x) - number_of_triangles(x)
independence_number(x) >= diameter(x)/different_degrees(x)
independence_number(x) >= ceil(order(x)/brooks(x))
independence_number(x) >= minimum(max_degree(x), floor(lovasz_theta(x)))
independence_number(x) >= -max_common_neighbors(x) + min_degree(x)
independence_number(x) >= max_degree(x) - order_automorphism_group(x)
independence_number(x) >= -card_periphery(x) + matching_number(x)
independence_number(x) >= minimum(min_degree(x), floor(lovasz_theta(x)))
independence_number(x) >= matching_number(x) - sigma_2(x) - 1
independence_number(x) >= matching_number(x) - order_automorphism_group(x) - 1
independence_number(x) >= -10^different_degrees(x) + matching_number(x)
independence_number(x) >= card_negative_eigenvalues(x) - sigma_2(x)
independence_number(x) >= floor(lovasz_theta(x))/vertex_con(x)
independence_number(x) >= 2*floor(arccosh(lovasz_theta(x)))
independence_number(x) >= minimum(floor(lovasz_theta(x)), tan(spanning_trees_count(x)))
independence_number(x) >= floor(tan(barrus_bound(x) - 1))
independence_number(x) >= floor(arccosh(lovasz_theta(x)))^2
independence_number(x) >= minimum(card_positive_eigenvalues(x), 2*card_zero_eigenvalues(x))
independence_number(x) >= barrus_bound(x) - maximum(card_center(x), card_positive_eigenvalues(x))
independence_number(x) >= -1/2*diameter(x) + lovasz_theta(x)
independence_number(x) >= floor(tan(floor(gutman_energy(x))))
independence_number(x) >= minimum(floor(lovasz_theta(x)), max_even_minus_even_horizontal(x) + 1)
0 8 5 Dodecahedron
1 5 4 Clebsch graph
2 9 5 c24
3 11 5 c26
4 24 5 c60
5 18 4 c6xc6
6 10 4 holton_mckay
7 4 3 sixfour
8 19 4 Tutte Graph
9 4 3 non_ham_over
10 4 3 throwing
11 4 3 throwing2
12 4 3 throwing3
13 8 5 Blanusa First Snark Graph
14 7 5 Blanusa Second Snark Graph
15 9 5 Flower Snark
16 11 4 Mycielski Graph 5
17 12 3 s13e
18 25 4 circulant_50_1_3
19 21 3 s22e
20 4 3 difficult11
21 10 6 Desargues Graph
22 9 5 Flower Snark
23 5 3 Frucht graph
24 15 5 Hoffman-Singleton graph
25 9 6 Pappus Graph
26 5 4 Grotzsch graph
27 27 8 Gray graph
28 7 6 Heawood graph
29 6 4 Herschel graph
30 12 7 Coxeter Graph
31 7 5 Brinkmann graph
32 15 8 Tutte-Coxeter graph
33 19 4 Tutte Graph
34 7 5 Robertson Graph
35 10 4 Folkman Graph
36 35 10 Balaban 10-cage
37 9 6 Pappus Graph
38 5 3 Tietze Graph
39 12 5 Sylvester Graph
40 21 5 Szekeres Snark Graph
41 8 6 Moebius-Kantor Graph
42 8 3 ryan
43 4 3 inp
44 6 3 p10k4
45 43 5 c100
46 10 3 starfish
47 4 3 Shrikhande graph
48 7 3 sylvester
49 5 3 edge_critical_11_1
50 5 3 edge_critical_11_2
51 6 3 pepper_residue_graph
52 5 3 ce5
53 4 3 flower_with_4_petals
54 6 3 paw_x_paw
55 6 3 triangle_star
56 5 3 ce8
57 6 3 ce10
58 5 3 binary_octahedron
independence_number(x) >= -average_distance(x) + ceil(lovasz_theta(x))
independence_number(x) >= 1/2*cvetkovic(x)
independence_number(x) >= diameter(x)/different_degrees(x)
independence_number(x) >= order(x)/brooks(x)
independence_number(x) >= order(x)/szekeres_wilf(x)
independence_number(x) >= -max_common_neighbors(x) + min_degree(x)
independence_number(x) >= max_degree(x) - order_automorphism_group(x)
independence_number(x) >= -card_periphery(x) + matching_number(x)
independence_number(x) >= minimum(min_degree(x), floor(lovasz_theta(x)))
independence_number(x) >= minimum(diameter(x), lovasz_theta(x))
independence_number(x) >= lovasz_theta(x)/radius(x)
independence_number(x) >= maximum(max_even_minus_even_horizontal(x), 1/2*lovasz_theta(x))
independence_number(x) >= maximum(critical_independence_number(x), 1/2*lovasz_theta(x))
independence_number(x) >= matching_number(x) - order_automorphism_group(x) - 1
independence_number(x) >= ceil(1/2*cvetkovic(x))
independence_number(x) >= card_positive_eigenvalues(x) - lovasz_theta(x)
independence_number(x) >= card_negative_eigenvalues(x) - sigma_2(x)
independence_number(x) >= minimum(max_degree(x), floor(lovasz_theta(x)))
independence_number(x) >= floor(1/2*card_positive_eigenvalues(x))
independence_number(x) >= minimum(lovasz_theta(x), tan(order(x)))
independence_number(x) >= maximum(residue(x), 1/2*lovasz_theta(x))
independence_number(x) >= floor(lovasz_theta(x))/vertex_con(x)
independence_number(x) >= matching_number(x) - sigma_2(x) - 1
independence_number(x) >= -10^different_degrees(x) + matching_number(x)
independence_number(x) >= 2*floor(arccosh(lovasz_theta(x)))
independence_number(x) >= minimum(floor(lovasz_theta(x)), tan(spanning_trees_count(x)))
independence_number(x) >= floor(arccosh(lovasz_theta(x)))^2
independence_number(x) >= minimum(card_positive_eigenvalues(x), 2*card_zero_eigenvalues(x))
independence_number(x) >= ceil(order(x)/brooks(x))
independence_number(x) >= -1/2*diameter(x) + lovasz_theta(x)
independence_number(x) >= floor(tan(barrus_bound(x) - 1))
independence_number(x) >= barrus_bound(x) - maximum(card_center(x), card_positive_eigenvalues(x))
independence_number(x) >= floor(tan(floor(gutman_energy(x))))
independence_number(x) >= minimum(floor(lovasz_theta(x)), max_even_minus_even_horizontal(x) + 1)
independence_number(x) >= order(x)/brooks(x)
loaded graph dc1024
loaded graph dc2048
loaded graph properties data file
loaded graph invariants data file
loaded graph dc1024
loaded graph dc2048
loaded graph properties data file
loaded graph invariants data file
independence_number(x) >= residue(x)
independence_number(x) >= max_even_minus_even_horizontal(x)
independence_number(x) >= floor(tan(barrus_bound(x) - 1))
independence_number(x) >= min_degree(x) - number_of_triangles(x)
independence_number(x) >= -diameter(x) + 2*residue(x)
independence_number(x) >= -max_common_neighbors(x) + min_degree(x)
independence_number(x) >= -card_periphery(x) + matching_number(x)
independence_number(x) >= maximum(diameter(x), residue(x))
independence_number(x) >= matching_number(x) - sigma_2(x) - 1
independence_number(x) >= lovasz_theta(x)/vertex_con(x)
independence_number(x) >= matching_number(x) - order_automorphism_group(x) - 1
independence_number(x) >= -10^different_degrees(x) + matching_number(x)
independence_number(x) >= card_negative_eigenvalues(x) - sigma_2(x)
independence_number(x) >= card_periphery(x) - maximum(card_center(x), max_even_minus_even_horizontal(x))
independence_number(x) >= -1/2*diameter(x) + lovasz_theta(x)
independence_number(x) >= 1/2*card_center(x) - 1/2*order_automorphism_group(x)
independence_number(x) >= floor(arcsinh(lovasz_theta(x)))^2
independence_number(x) >= minimum(floor(lovasz_theta(x)), tan(spanning_trees_count(x)))
independence_number(x) >= minimum(card_positive_eigenvalues(x), 2*card_zero_eigenvalues(x))
independence_number(x) >= minimum(floor(lovasz_theta(x)), max_even_minus_even_horizontal(x) + 1)
73
1 1 k3
1 1 k4
1 1 k5
8 5 Dodecahedron
3 3 c8chorded
5 2 Clebsch graph
9 5 c24
11 6 c26
24 9 c60
18 6 c6xc6
10 6 holton_mckay
4 4 sixfour
2 2 c4
4 2 Petersen graph
1 1 p2
19 8 Tutte Graph
4 4 throwing
4 4 throwing2
4 4 throwing3
8 4 Blanusa First Snark Graph
7 4 Blanusa Second Snark Graph
9 4 Flower Snark
3 3 ryan3
1 1 k10
25 9 circulant_50_1_3
4 2 Chvatal graph
10 5 Desargues Graph
9 4 Flower Snark
5 4 Frucht graph
15 2 Hoffman-Singleton graph
2 2 Octahedron
3 2 Thomsen graph
4 2 Petersen graph
9 4 Pappus Graph
27 6 Gray graph
7 3 Heawood graph
12 4 Coxeter Graph
7 3 Brinkmann graph
15 4 Tutte-Coxeter graph
19 8 Tutte Graph
7 3 Robertson Graph
10 4 Folkman Graph
35 6 Balaban 10-cage
9 4 Pappus Graph
5 3 Tietze Graph
12 3 Sylvester Graph
21 7 Szekeres Snark Graph
8 4 Moebius-Kantor Graph
8 8 ryan
3 3 regular_non_trans
43 12 c100
4 2 Shrikhande graph
7 6 sylvester
2 2 c5
3 3 c6
4 4 c9
4 3 ce3
5 2 ce5
3 2 Wagner Graph
5 4 binary_octahedron
2 2 prism
1 1 alpha_critical_A_
1 1 alpha_critical_Bw
1 1 alpha_critical_C~
2 2 alpha_critical_Dhc
1 1 alpha_critical_D~{
1 1 alpha_critical_E~~w
3 3 alpha_critical_FhCKG
1 1 alpha_critical_F~~~w
2 2 alpha_critical_GbMmvG
1 1 alpha_critical_G~~~~{
4 4 alpha_critical_HhCGGE@
1 1 alpha_critical_H~~~~~~
couldn't load dc1024_g6string.sobj
couldn't load dc2048_g6string.sobj
can't load graph properties sobj file
can't load graph invariant sobj file
independence_number(x) >= maximum(residue(x), 1/2*lovasz_theta(x))
independence_number(x) >= ceil(1/2*lovasz_theta(x))
independence_number(x) >= order(x)/szekeres_wilf(x)
independence_number(x) >= welsh_powell(x)/card_periphery(x)
independence_number(x) >= floor(tan(log(barrus_bound(x))/log(10)))
independence_number(x) >= maximum(max_even_minus_even_horizontal(x), 1/2*lovasz_theta(x))
independence_number(x) >= -card_center(x) + floor(lovasz_theta(x))
independence_number(x) >= (barrus_bound(x) - 1)/card_periphery(x)
independence_number(x) >= maximum(critical_independence_number(x), 1/2*lovasz_theta(x))
independence_number(x) >= -10^max_common_neighbors(x) + matching_number(x)
independence_number(x) >= barrus_bound(x) - maximum(card_center(x), card_positive_eigenvalues(x))
independence_number(x) >= (residue(x) - 1)^min_common_neighbors(x)
independence_number(x) >= floor(lovasz_theta(x))/vertex_con(x)
independence_number(x) >= floor(tan(barrus_bound(x) - 1))
independence_number(x) >= -brinkmann_steffen(x) + card_negative_eigenvalues(x)
independence_number(x) >= matching_number(x) - sigma_2(x) - 1
independence_number(x) >= -max_common_neighbors(x) + min_degree(x) - 1
independence_number(x) >= floor(sqrt(barrus_bound(x)))
independence_number(x) >= ceil(log(barrus_bound(x)))
independence_number(x) >= 2*floor(arccosh(lovasz_theta(x)))
independence_number(x) >= sqrt(szeged_index(x))/gutman_energy(x)
independence_number(x) >= maximum(radius(x), 1/2*lovasz_theta(x))
independence_number(x) >= minimum(floor(lovasz_theta(x)), tan(spanning_trees_count(x)))
independence_number(x) >= floor(arccosh(lovasz_theta(x)))^2
independence_number(x) >= -card_periphery(x) + min_degree(x) - 1
independence_number(x) >= -min_common_neighbors(x) + 1/2*min_degree(x)
independence_number(x) >= sqrt(cycle_space_dimension(x)) - number_of_triangles(x)
independence_number(x) >= 2*fractional_alpha(x)/szekeres_wilf(x)
independence_number(x) >= minimum(sum_temperatures(x), card_negative_eigenvalues(x) - number_of_triangles(x))
independence_number(x) >= 1/2*card_negative_eigenvalues(x) - max_common_neighbors(x)
independence_number(x) >= -number_of_triangles(x)^average_vertex_temperature(x) + max_degree(x)
independence_number(x) >= -2*card_center(x) + cvetkovic(x)
independence_number(x) >= ceil(1/2*lovasz_theta(x) + 1/2)
independence_number(x) >= ceil(log(lovasz_theta(x)^2))
independence_number(x) >= -(card_negative_eigenvalues(x) - card_positive_eigenvalues(x))*card_zero_eigenvalues(x)
independence_number(x) >= floor(tan(floor(gutman_energy(x))))
independence_number(x) >= floor(tan(e^card_positive_eigenvalues(x)))
independence_number(x) >= minimum(floor(lovasz_theta(x)), max_even_minus_even_horizontal(x) + 1)
66
2
2.236068
loaded graph dc1024
loaded graph dc2048
loaded graph properties data file
loaded graph invariants data file
independence_number(x) >= maximum(max_even_minus_even_horizontal(x), 1/2*lovasz_theta(x))
independence_number(x) >= 1/2*cvetkovic(x)
independence_number(x) >= sqrt(barrus_bound(x))
independence_number(x) >= order(x)/brooks(x)
independence_number(x) >= -max_common_neighbors(x) + min_degree(x)
independence_number(x) >= -card_periphery(x) + matching_number(x)
independence_number(x) >= -1/2*diameter(x) + lovasz_theta(x)
independence_number(x) >= lovasz_theta(x)/vertex_con(x)
independence_number(x) >= -diameter(x) + 2*residue(x)
independence_number(x) >= matching_number(x) - order_automorphism_group(x) - 1
independence_number(x) >= minimum(cvetkovic(x), inverse_degree(x))
independence_number(x) >= card_positive_eigenvalues(x) - lovasz_theta(x)
independence_number(x) >= card_negative_eigenvalues(x) - sigma_2(x)
independence_number(x) >= minimum(lovasz_theta(x), tan(order(x)))
independence_number(x) >= ceil(sqrt(barrus_bound(x)))
independence_number(x) >= ceil(1/2*cvetkovic(x))
independence_number(x) >= -card_periphery(x) + 2*diameter(x)
independence_number(x) >= matching_number(x) - sigma_2(x) - 1
independence_number(x) >= -10^different_degrees(x) + matching_number(x)
independence_number(x) >= card_periphery(x) - maximum(card_center(x), max_even_minus_even_horizontal(x))
independence_number(x) >= 1/2*card_center(x) - 1/2*order_automorphism_group(x)
independence_number(x) >= floor(tan(barrus_bound(x) - 1))
independence_number(x) >= floor(arcsinh(lovasz_theta(x)))^2
independence_number(x) >= minimum(floor(lovasz_theta(x)), tan(spanning_trees_count(x)))
independence_number(x) >= minimum(card_positive_eigenvalues(x), 2*card_zero_eigenvalues(x))
independence_number(x) >= minimum(floor(lovasz_theta(x)), max_even_minus_even_horizontal(x) + 1)
1 1 k3
1 1 k4
1 1 k5
6 6 Dodecahedron
2 2 c8chorded
3 3 Clebsch graph
8 8 c24
8 8 c26
20 20 c60
9 9 c6xc6
8 8 holton_mckay
3 3 sixfour
2 2 c4
3 3 Petersen graph
1 1 p2
15 15 Tutte Graph
2 2 throwing
3 3 throwing2
3 3 throwing3
6 6 Blanusa First Snark Graph
6 6 Blanusa Second Snark Graph
6 6 Flower Snark
2 2 ryan3
1 1 k10
12 12 circulant_50_1_3
3 3 Chvatal graph
6 6 Desargues Graph
6 6 Flower Snark
4 4 Frucht graph
7 7 Hoffman-Singleton graph
1 1 Octahedron
2 2 Thomsen graph
3 3 Petersen graph
6 6 Pappus Graph
18 18 Gray graph
4 4 Heawood graph
9 9 Coxeter Graph
5 5 Brinkmann graph
10 10 Tutte-Coxeter graph
15 15 Tutte Graph
4 4 Robertson Graph
5 5 Folkman Graph
23 23 Balaban 10-cage
6 6 Pappus Graph
4 4 Tietze Graph
7 7 Sylvester Graph
16 16 Szekeres Snark Graph
5 5 Moebius-Kantor Graph
8 8 ryan
2 2 regular_non_trans
33 33 c100
2 2 Shrikhande graph
5 5 sylvester
5/3 2 c5
3 3 c6
3 3 c9
2 2 ce3
3 3 ce5
2 2 Wagner Graph
3 3 binary_octahedron
2 2 prism
1 1 alpha_critical_A_
1 1 alpha_critical_Bw
1 1 alpha_critical_C~
5/3 2 alpha_critical_Dhc
1 1 alpha_critical_D~{
1 1 alpha_critical_E~~w
7/3 3 alpha_critical_FhCKG
1 1 alpha_critical_F~~~w
2 2 alpha_critical_GbMmvG
1 1 alpha_critical_G~~~~{
3 3 alpha_critical_HhCGGE@
1 1 alpha_critical_H~~~~~~
8 7 Dodecahedron
9 8 c24
11 9 c26
24 21 c60
4 3 Petersen graph
19 17 Tutte Graph
8 7 Blanusa First Snark Graph
7 6 Blanusa Second Snark Graph
15 7 Hoffman-Singleton graph
4 3 Petersen graph
12 10 Coxeter Graph
7 5 Brinkmann graph
19 17 Tutte Graph
7 4 Robertson Graph
12 7 Sylvester Graph
21 19 Szekeres Snark Graph
43 40 c100
4 3 Shrikhande graph
5 3 ce5
5 4 binary_octahedron
loaded graph dc1024
loaded graph dc2048
loaded graph properties data file
loaded graph invariants data file
independence_number(x) >= maximum(max_even_minus_even_horizontal(x), 1/2*lovasz_theta(x))
independence_number(x) >= floor(tan(log(barrus_bound(x))/log(10)))
independence_number(x) >= diameter(x)/different_degrees(x)
independence_number(x) >= order(x)/brooks(x)
independence_number(x) >= (barrus_bound(x) - 1)/card_periphery(x)
independence_number(x) >= minimum(diameter(x), lovasz_theta(x))
independence_number(x) >= -card_center(x) + floor(lovasz_theta(x))
independence_number(x) >= -10^max_common_neighbors(x) + matching_number(x)
independence_number(x) >= maximum(critical_independence_number(x), 1/2*lovasz_theta(x))
independence_number(x) >= (residue(x) - 1)^min_common_neighbors(x)
independence_number(x) >= barrus_bound(x) - maximum(card_center(x), card_positive_eigenvalues(x))
independence_number(x) >= floor(tan(barrus_bound(x) - 1))
independence_number(x) >= -brinkmann_steffen(x) + card_negative_eigenvalues(x)
independence_number(x) >= minimum(floor(lovasz_theta(x)), tan(spanning_trees_count(x)))
independence_number(x) >= -max_common_neighbors(x) + min_degree(x) - 1
independence_number(x) >= maximum(residue(x), 1/2*lovasz_theta(x))
independence_number(x) >= floor(lovasz_theta(x))/vertex_con(x)
independence_number(x) >= minimum(lovasz_theta(x), tan(order(x)))
independence_number(x) >= 2*floor(arccosh(lovasz_theta(x)))
independence_number(x) >= sqrt(szeged_index(x))/gutman_energy(x)
independence_number(x) >= minimum(welsh_powell(x), card_negative_eigenvalues(x)) - number_of_triangles(x)
independence_number(x) >= -card_periphery(x) + min_degree(x) - 1
independence_number(x) >= -min_common_neighbors(x) + 1/2*min_degree(x)
independence_number(x) >= sqrt(cycle_space_dimension(x)) - number_of_triangles(x)
independence_number(x) >= matching_number(x) - sigma_2(x) - 1
independence_number(x) >= floor(arccosh(lovasz_theta(x)))^2
independence_number(x) >= -2*card_center(x) + cvetkovic(x)
independence_number(x) >= 1/2*card_negative_eigenvalues(x) - max_common_neighbors(x)
independence_number(x) >= -number_of_triangles(x)^average_vertex_temperature(x) + max_degree(x)
independence_number(x) >= ceil(order(x)/brooks(x))
independence_number(x) >= ceil(log(lovasz_theta(x)^2))
independence_number(x) >= -(card_negative_eigenvalues(x) - card_positive_eigenvalues(x))*card_zero_eigenvalues(x)
independence_number(x) >= floor(tan(floor(gutman_energy(x))))
independence_number(x) >= floor(tan(e^card_positive_eigenvalues(x)))
independence_number(x) >= minimum(floor(lovasz_theta(x)), max_even_minus_even_horizontal(x) + 1)
True
loaded graph dc1024
loaded graph dc2048
loaded graph properties data file
loaded graph invariants data file
independence_number(x) >= maximum(max_even_minus_even_horizontal(x), 1/2*lovasz_theta(x))
independence_number(x) >= sqrt(barrus_bound(x))
independence_number(x) >= order(x)/brooks(x)
independence_number(x) >= -max_common_neighbors(x) + min_degree(x)
independence_number(x) >= -card_periphery(x) + matching_number(x)
independence_number(x) >= -1/2*diameter(x) + lovasz_theta(x)
independence_number(x) >= 1/2*card_center(x) - 1/2*order_automorphism_group(x)
independence_number(x) >= lovasz_theta(x)/vertex_con(x)
independence_number(x) >= -diameter(x) + 2*residue(x)
independence_number(x) >= matching_number(x) - order_automorphism_group(x) - 1
independence_number(x) >= minimum(cvetkovic(x), inverse_degree(x))
independence_number(x) >= card_positive_eigenvalues(x) - lovasz_theta(x)
independence_number(x) >= card_negative_eigenvalues(x) - sigma_2(x)
independence_number(x) >= minimum(lovasz_theta(x), tan(order(x)))
independence_number(x) >= residue(x)
independence_number(x) >= ceil(sqrt(barrus_bound(x)))
independence_number(x) >= -card_periphery(x) + 2*diameter(x)
independence_number(x) >= matching_number(x) - sigma_2(x) - 1
independence_number(x) >= -10^different_degrees(x) + matching_number(x)
independence_number(x) >= card_periphery(x) - maximum(card_center(x), max_even_minus_even_horizontal(x))
independence_number(x) >= floor(arcsinh(lovasz_theta(x)))^2
independence_number(x) >= floor(tan(barrus_bound(x) - 1))
independence_number(x) >= minimum(floor(lovasz_theta(x)), tan(spanning_trees_count(x)))
independence_number(x) >= minimum(card_positive_eigenvalues(x), 2*card_zero_eigenvalues(x))
independence_number(x) >= minimum(floor(lovasz_theta(x)), max_even_minus_even_horizontal(x) + 1)
loaded graph dc1024
loaded graph dc2048
loaded graph properties data file
loaded graph invariants data file
1 1 k3
1 1 k4
1 1 k5
8 5 Dodecahedron
3 3 c8chorded
5 2 Clebsch graph
9 5 c24
11 6 c26
24 9 c60
18 6 c6xc6
10 6 holton_mckay
4 4 sixfour
2 2 c4
4 2 Petersen graph
1 1 p2
19 8 Tutte Graph
4 4 throwing
4 4 throwing2
4 4 throwing3
8 4 Blanusa First Snark Graph
7 4 Blanusa Second Snark Graph
9 4 Flower Snark
3 3 ryan3
1 1 k10
25 9 circulant_50_1_3
4 2 Chvatal graph
10 5 Desargues Graph
9 4 Flower Snark
5 4 Frucht graph
15 2 Hoffman-Singleton graph
2 2 Octahedron
3 2 Thomsen graph
4 2 Petersen graph
9 4 Pappus Graph
27 6 Gray graph
7 3 Heawood graph
12 4 Coxeter Graph
7 3 Brinkmann graph
15 4 Tutte-Coxeter graph
19 8 Tutte Graph
7 3 Robertson Graph
10 4 Folkman Graph
35 6 Balaban 10-cage
9 4 Pappus Graph
5 3 Tietze Graph
12 3 Sylvester Graph
21 7 Szekeres Snark Graph
8 4 Moebius-Kantor Graph
8 8 ryan
3 3 regular_non_trans
43 12 c100
4 2 Shrikhande graph
7 6 sylvester
2 2 c5
3 3 c6
4 4 c9
4 3 ce3
5 2 ce5
3 2 Wagner Graph
5 4 binary_octahedron
2 2 prism
1 1 alpha_critical_A_
1 1 alpha_critical_Bw
1 1 alpha_critical_C~
2 2 alpha_critical_Dhc
1 1 alpha_critical_D~{
1 1 alpha_critical_E~~w
3 3 alpha_critical_FhCKG
1 1 alpha_critical_F~~~w
2 2 alpha_critical_GbMmvG
1 1 alpha_critical_G~~~~{
4 4 alpha_critical_HhCGGE@
1 1 alpha_critical_H~~~~~~
couldn't load dc1024_g6string.sobj
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independence_number(x) >= (barrus_bound(x) - 1)/card_periphery(x)
independence_number(x) >= minimum(diameter(x), card_periphery(x))
independence_number(x) >= diameter(x) - different_degrees(x)
independence_number(x) >= order(x)/brooks(x)
independence_number(x) >= order(x)/szekeres_wilf(x)
independence_number(x) >= minimum(floor(lovasz_theta(x)), tan(spanning_trees_count(x)))
independence_number(x) >= maximum(max_even_minus_even_horizontal(x), 1/2*lovasz_theta(x))
independence_number(x) >= -card_center(x) + floor(lovasz_theta(x))
independence_number(x) >= maximum(critical_independence_number(x), 1/2*lovasz_theta(x))
independence_number(x) >= -10^max_common_neighbors(x) + matching_number(x)
independence_number(x) >= cos(spanning_trees_count(x))*floor(lovasz_theta(x))
independence_number(x) >= welsh_powell(x)/card_periphery(x)
independence_number(x) >= (residue(x) - 1)^min_common_neighbors(x)
independence_number(x) >= -max_common_neighbors(x) + min_degree(x) - 1
independence_number(x) >= -brinkmann_steffen(x) + card_negative_eigenvalues(x)
independence_number(x) >= minimum(welsh_powell(x), card_negative_eigenvalues(x)) - number_of_triangles(x)
independence_number(x) >= maximum(residue(x), 1/2*lovasz_theta(x))
independence_number(x) >= minimum(matching_number(x), diameter(x) - 1)
independence_number(x) >= minimum(fractional_alpha(x), diameter(x) - 1)
independence_number(x) >= floor(tan(barrus_bound(x) - 1))
independence_number(x) >= minimum(lovasz_theta(x), tan(order(x)))
independence_number(x) >= floor(lovasz_theta(x))/vertex_con(x)
independence_number(x) >= sqrt(szeged_index(x))/gutman_energy(x)
independence_number(x) >= 2*floor(arccosh(lovasz_theta(x)))
independence_number(x) >= floor(tan(floor(gutman_energy(x))))
independence_number(x) >= -card_periphery(x) + min_degree(x) - 1
independence_number(x) >= -min_common_neighbors(x) + 1/2*min_degree(x)
independence_number(x) >= sqrt(cycle_space_dimension(x)) - number_of_triangles(x)
independence_number(x) >= matching_number(x) - sigma_2(x) - 1
independence_number(x) >= floor(arccosh(lovasz_theta(x)))^2
independence_number(x) >= 2*fractional_alpha(x)/szekeres_wilf(x)
independence_number(x) >= ceil(order(x)/brooks(x))
independence_number(x) >= 1/2*card_negative_eigenvalues(x) - max_common_neighbors(x)
independence_number(x) >= -number_of_triangles(x)^average_vertex_temperature(x) + max_degree(x)
independence_number(x) >= -2*card_center(x) + cvetkovic(x)
independence_number(x) >= ceil(log(lovasz_theta(x)^2))
independence_number(x) >= -(card_negative_eigenvalues(x) - card_positive_eigenvalues(x))*card_zero_eigenvalues(x)
independence_number(x) >= floor(tan(e^card_positive_eigenvalues(x)))
independence_number(x) >= floor(tan(log(barrus_bound(x))/log(10)))
independence_number(x) >= minimum(floor(lovasz_theta(x)), max_even_minus_even_horizontal(x) + 1)
32
independence_number(x) >= diameter(x) - different_degrees(x)
True
1/2
[ 1 1 0 0 0 1 1/5*sqrt(5)]
[ 1 0 1 1 0 0 1/5*sqrt(5)]
[ 0 1 0 0 1 0 1/5*sqrt(5)]
[ 1 0 1 0 0 1 1/5*sqrt(5)]
[ 0 0 0 1 1 0 1/5*sqrt(5)]
[ 1 0 0 0 0 2 1/5*sqrt(5)]
[ 0 1 0 0 0 -1 0]
[ 0 0 1 0 0 -1 0]
[ 0 0 0 1 0 -1 0]
[ 0 0 0 0 1 1 1/5*sqrt(5)]
[ 1 0 0 0 0 0 sqrt(5) - 2]
[ 0 1 0 0 0 0 -2/5*sqrt(5) + 1]
[ 0 0 1 0 0 0 -2/5*sqrt(5) + 1]
[ 0 0 0 1 0 0 -2/5*sqrt(5) + 1]
[ 0 0 0 0 1 0 3/5*sqrt(5) - 1]
[ 0 0 0 0 0 1 -2/5*sqrt(5) + 1]
[0.236067977499790]
[0.105572809000084]
[0.105572809000084]
[0.105572809000084]
[0.341640786499874]
[0.105572809000084]