Graphs Invariants API

The graph invariants modules provide functions for computing classical, structural, spectral, domination-related, and other graph-theoretic quantities.

• classics
• Classics
  • arboricity()
  • average_distance()
  • bipartite_number()
  • chromatic_number()
  • clique_number()
  • edge_cover_number()
  • independence_number()
  • is_hamiltonian()
  • linear_arboricity()
  • matching_number()
  • maximum_clique()
  • maximum_independent_set()
  • maximum_induced_bipartite_subgraph()
  • maximum_matching()
  • minimum_edge_cover()
  • minimum_vertex_cover()
  • optimal_proper_coloring()
  • path_cover_number()
  • triameter()
  • vertex_clique_cover_number()
  • vertex_clique_cover_partition()
  • vertex_cover_number()
• coloring predicates
• Coloring Predicates
  • can_edge_color_with_k()
  • is_class1()
  • is_class2()
• core invariants
• Core Invariants
  • alpha_core_number()
  • alpha_core_set()
  • clique_core_number()
  • clique_core_set()
  • core_number_maximum_fast()
  • core_number_minimum()
  • core_set_maximum_fast()
  • core_set_minimum()
  • domination_core_number()
  • domination_core_set()
  • zero_forcing_core_number()
  • zero_forcing_core_set()
• critical invariants
• Critical Invariants
  • domination_edge_change_number()
  • domination_edge_decrease_number()
  • domination_edge_increase_number()
  • domination_edge_max_jump()
  • domination_edge_same_number()
  • domination_vertex_change_number()
  • domination_vertex_decrease_number()
  • domination_vertex_increase_number()
  • domination_vertex_max_jump()
  • domination_vertex_same_number()
  • edge_critical_number()
  • edge_deletion_deltas()
  • vertex_critical_number()
  • vertex_critical_set()
  • vertex_deletion_deltas()
  • vertex_deletion_max_jump()
• cycle invariants
• Cycle Invariants
  • circumference()
  • cycle_rank()
  • decycling_number()
  • even_girth()
  • feedback_vertex_number()
  • feedback_vertex_set()
  • girth()
  • maximum_induced_forest_number()
  • maximum_number_of_vertex_disjoint_cycles()
  • odd_girth()
  • triangle_count()
• degree
• Degree
  • annihilation_number()
  • average_degree()
  • count_of_maximum_degree_vertices()
  • count_of_minimum_degree_vertices()
  • degree()
  • degree_sequence()
  • distinct_degree_count()
  • irregularity()
  • k_residue()
  • k_residue_from_degrees()
  • maximum_degree()
  • minimum_degree()
  • n1_degree_count()
  • residue()
  • residue_from_degrees()
  • slater()
  • sub_k_domination_number()
  • sub_total_domination_number()
• domination
• Domination
  • complement_is_connected()
  • connected_domination_number()
  • domination_number()
  • double_roman_domination_number()
  • independent_domination_number()
  • is_dominating_set()
  • is_outer_connected_dominating_set()
  • min_maximal_matching_number()
  • minimum_connected_dominating_set()
  • minimum_dominating_set()
  • minimum_double_roman_dominating_function()
  • minimum_independent_dominating_set()
  • minimum_outer_connected_dominating_set()
  • minimum_rainbow_dominating_function()
  • minimum_restrained_dominating_set()
  • minimum_roman_dominating_function()
  • minimum_total_domination_set()
  • outer_connected_domination_number()
  • rainbow_domination_number()
  • restrained_domination_number()
  • roman_domination_number()
  • three_rainbow_domination_number()
  • total_domination_number()
  • two_rainbow_domination_number()
• graph indices
• Graph Indices
  • abc_index()
  • augmented_zagreb_index()
  • ga_index()
  • harmonic_index()
  • hyper_zagreb_index()
  • randic_index()
  • reciprocal_augmented_zagreb_index()
  • reciprocal_ga_index()
  • reciprocal_hyper_zagreb_index()
  • reciprocal_sombor_index()
  • reciprocal_zagreb_1()
  • reciprocal_zagreb_2()
  • sombor_index()
  • sum_connectivity_index()
  • zagreb_1()
  • zagreb_2()
• local invariants
• Local Invariants
  • local_annihilation_number()
  • local_chromatic_number()
  • local_clique_number()
  • local_domination_number()
  • local_harmonic_index()
  • local_independence_number()
  • local_parameter()
  • local_parameter_radius()
  • local_residue()
  • local_zero_forcing_number()
• spectral
• Spectral
  • AdjacencyInertia
  • adjacency_eigenvalues()
  • adjacency_graph_energy()
  • adjacency_inertia_triple()
  • adjacency_matrix()
  • adjacency_negative_inertia_index()
  • adjacency_nullity()
  • adjacency_positive_inertia_index()
  • adjacency_rank()
  • adjacency_signature()
  • adjacency_smallest_positive_eigenvalue()
  • adjacency_zero_inertia_index()
  • algebraic_connectivity()
  • laplacian_eigenvalues()
  • laplacian_matrix()
  • largest_laplacian_eigenvalue()
  • second_largest_adjacency_eigenvalue()
  • smallest_adjacency_eigenvalue()
  • spectral_radius()
  • zero_adjacency_eigenvalues_count()
• transversal invariants
• Transversal Invariants
  • maximal_clique_transversal_number()
  • maximal_independent_set_transversal_number()
  • minimal_dominating_set_transversal_number()
• zero forcing
• Zero Forcing
  • burning_number()
  • compute_well_splitting_number()
  • connected_k_forcing_number()
  • connected_zero_forcing_number()
  • is_connected_k_forcing_set()
  • is_connected_zero_forcing_set()
  • is_k_forcing_active_set()
  • is_k_forcing_set()
  • is_k_forcing_vertex()
  • is_k_power_dominating_set()
  • is_power_dominating_set()
  • is_psd_forcing_vertex()
  • is_psd_zero_forcing_set()
  • is_total_zero_forcing_set()
  • is_well_splitting_set()
  • is_zero_forcing_set()
  • is_zero_forcing_vertex()
  • k_forcing_number()
  • k_power_domination_number()
  • minimum_connected_k_forcing_set()
  • minimum_connected_zero_forcing_set()
  • minimum_k_forcing_set()
  • minimum_k_power_dominating_set()
  • minimum_power_dominating_set()
  • minimum_psd_zero_forcing_set()
  • minimum_total_zero_forcing_set()
  • minimum_zero_forcing_set()
  • positive_semidefinite_zero_forcing_number()
  • power_domination_number()
  • psd_color_change()
  • total_zero_forcing_number()
  • two_forcing_number()
  • well_splitting_number()
  • zero_forcing_number()
• Advanced Coloring Invariants API
• Advanced Coloring Invariants
  • EdgeColoringSolveResult
  • SolveResult
  • has_open_neighborhood_conflict_free_coloring()
  • has_open_neighborhood_odd_coloring()
  • has_proper_open_neighborhood_conflict_free_coloring()
  • has_rainbow_connection_coloring()
  • has_strong_rainbow_connection_coloring()
  • open_neighborhood_conflict_free_chromatic_number()
  • open_neighborhood_conflict_free_coloring()
  • open_neighborhood_odd_chromatic_number()
  • open_neighborhood_odd_coloring()
  • proper_open_neighborhood_conflict_free_chromatic_number()
  • proper_open_neighborhood_conflict_free_coloring()
  • rainbow_connection_coloring()
  • rainbow_connection_number()
  • strong_rainbow_connection_coloring()
  • strong_rainbow_connection_number()