- Introduction
- Construction of Graphs and Digraphs
- Graphs with a Sparse Representation
- The Vertex--Set and Edge--Set of a Graph
- Labelled, Capacitated and Weighted Graphs
- Standard Constructions for Graphs
- Subgraphs and Quotient Graphs
- Incremental Construction of Graphs
- Adding Vertices
- Removing Vertices
- Adding Edges
- G + { u, v } : GrphUnd, { GrphVert, GrphVert }-> GrphUnd, GrphEdge
- G + { { u, v } } : GrphUnd, { { GrphVert, GrphVert } } -> GrphUnd
- G +:= { u, v } : GrphUnd, { GrphVert, GrphVert } ->
- AddEdge(G, u, v) : Grph, GrphVert, GrphVert -> Grph, GrphEdge
- AddEdge(G, u, v, l) : Grph, GrphVert, GrphVert, . -> Grph, GrphEdge
- AddEdge(~G, u, v) : Grph, GrphVert, GrphVert ->
- AddEdges(G, S) : GrphUnd, { { GrphVert, GrphVert } } -> GrphUnd
- AddEdges(G, S, L) : Grph, SeqEnum, SeqEnum -> Grph
- AddEdges(~G, S) : GrphUnd, { { GrphVert, GrphVert } } ->
- Removing Edges
- Constructing Complements, Line Graphs; Contraction, Switching
- Unions and Products of Graphs
- Union(G, H) : GrphUnd, GrphUnd -> GrphUnd
- EdgeUnion(G, H) : GrphDir, GrphDir -> GrphDir
- CompleteUnion(G, H) : GrphDir, GrphDir -> GrphDir
- CartesianProduct(G, H) : GrphDir, GrphDir -> GrphDir
- LexProduct(G, H) : GrphDir, GrphDir -> GrphDir
- TensorProduct(G, H) : GrphDir, GrphDir -> GrphDir
- G ^ n : GrphUnd, RngIntElt -> GrphUnd
- Converting between Graphs and Digraphs
- Construction from Groups, Codes and Designs
- Graphs Constructed from Groups
- CayleyGraph(A : parameter) : Grp -> Grph, GrphVertSet, GrphEdgeSet
- SchreierGraph(A, B) : Grp, Grp -> Grph, GrphVertSet, GrphEdgeSet
- OrbitalGraph(P, u, T) : GrpPerm, RngIntElt, { RngIntElt } -> GrphUnd
- ClosureGraph(P, G) : GrpPerm, GrphUnd -> GrphUnd
- PaleyGraph(q) : RngIntElt -> GrphUnd
- PaleyTournament(q) : RngIntElt -> GrphDir
- Graphs Constructed from Designs
- Miscellaneous Graph Constructions
- Elementary Invariants of a Graph
- Elementary Graph Predicates
- Adjacency and Degree
- Connectedness
- Distances, Paths and Circuits in a Graph
- Maximum Flow, Minimum Cut, and Shortest Paths
- Matrices and Vector Spaces Associated with a Graph or Digraph
- Spanning Trees of a Graph or Digraph
- Directed Trees
- Colourings
- Cliques, Independent Sets
- HasClique(G, k) : GrphUnd, RngIntElt -> BoolElt, { GrphVert }
- HasClique(G, k, m : parameters) : GrphUnd, RngIntElt, BoolElt -> BoolElt, { GrphVert }
- HasClique(G, k, m, f : parameters) : GrphUnd, RngIntElt, BoolElt, RngIntElt -> BoolElt, { GrphVert }
- MaximumClique(G : parameters) : GrphUnd -> { GrphVert }
- CliqueNumber(G : parameters) : GrphUnd -> RngIntElt
- AllCliques(G : parameters) : GrphUnd -> SeqEnum
- AllCliques(G, k : parameters) : GrphUnd, RngIntElt -> SeqEnum
- AllCliques(G, k, m : parameters) : GrphUnd, RngIntElt, BoolElt -> SeqEnum
- MaximumIndependentSet(G: parameters) : GrphUnd -> { GrphVert }
- IndependenceNumber(G: parameters) : GrphUnd -> RngIntElt
- Example Graph_Cliques (H158E16)
- Planar Graphs
- Automorphism Group of a Graph or Digraph
- The Automorphism Group Function
- nauty Invariants
- Graph Colouring and Automorphism Group
- Variants of Automorphism Group
- Action of Automorphisms
- Image(a, Y, y) : GrpPermElt, GSet, Elt -> Elt
- Orbit(A, Y, y) : GrpPerm, GSet, Elt -> GSet
- Orbits(A, Y) : GrpPerm, GSet -> [ GSet ]
- Stabilizer(A, Y, y) : GrpPerm, GSet, Elt -> GrpPerm
- Action(A, Y) : GrpPerm, GSet -> Hom(Grp), GrpPerm, GrpPerm
- ActionImage(A, Y) : GrpPerm, GSet -> GrpPerm
- ActionKernel(A, Y) : GrpPerm, GSet -> GrpPerm
- Example Graph_AutomorphismAction (H158E20)
- Symmetry and Regularity Properties of Graphs
- Graph Databases and Graph Generation
- Strongly Regular Graphs
- StronglyRegularGraphsDatabase() : -> DB
- Classes(D) : DB -> SeqEnum
- NumberOfClasses(D) : DB -> RngIntElt
- NumberOfGraphs(D) : DB -> RngIntElt
- NumberOfGraphs(D, S) : DB, SeqEnum -> RngIntElt
- Graphs(D, S) : DB, SeqEnum -> SeqEnum
- Graph(D, S, i) : DB, SeqEnum, RngIntElt -> GrphUnd
- RandomGraph(D) : DB -> GrphUnd
- RandomGraph(D, S) : DB, SeqEnum -> GrphUnd
- for G in D do ... end for;
- Example Graph_StronglyRegularGraphs (H158E22)
- Small Graphs
- Generating Graphs
- A General Facility
- Bibliography
V2.28, 13 July 2023