\chapcontents {1}{Grape}{5} \seccontents {1.1}{Installing the GRAPE Package} {5} \seccontents {1.2}{Loading GRAPE} {6} \seccontents {1.3}{The structure of a graph in GRAPE} {7} \seccontents {1.4}{Examples of the use of GRAPE} {7} \chapcontents {2}{Functions to construct and modify graphs}{9} \seccontents {2.1}{Graph} {9} \seccontents {2.2}{EdgeOrbitsGraph} {10} \seccontents {2.3}{NullGraph} {10} \seccontents {2.4}{CompleteGraph} {11} \seccontents {2.5}{JohnsonGraph} {11} \seccontents {2.6}{CayleyGraph} {11} \seccontents {2.7}{AddEdgeOrbit} {12} \seccontents {2.8}{RemoveEdgeOrbit} {13} \seccontents {2.9}{AssignVertexNames} {13} \chapcontents {3}{Functions to inspect graphs, vertices and edges}{15} \seccontents {3.1}{IsGraph} {15} \seccontents {3.2}{OrderGraph} {15} \seccontents {3.3}{IsVertex} {15} \seccontents {3.4}{VertexName} {15} \seccontents {3.5}{VertexNames} {16} \seccontents {3.6}{Vertices} {16} \seccontents {3.7}{VertexDegree} {16} \seccontents {3.8}{VertexDegrees} {16} \seccontents {3.9}{IsLoopy} {16} \seccontents {3.10}{IsSimpleGraph} {17} \seccontents {3.11}{Adjacency} {17} \seccontents {3.12}{IsEdge} {17} \seccontents {3.13}{DirectedEdges} {17} \seccontents {3.14}{UndirectedEdges} {18} \seccontents {3.15}{Distance} {18} \seccontents {3.16}{Diameter} {18} \seccontents {3.17}{Girth} {19} \seccontents {3.18}{IsConnectedGraph} {19} \seccontents {3.19}{IsBipartite} {19} \seccontents {3.20}{IsNullGraph} {20} \seccontents {3.21}{IsCompleteGraph} {20} \chapcontents {4}{Functions to determine regularity properties of graphs}{21} \seccontents {4.1}{IsRegularGraph} {21} \seccontents {4.2}{LocalParameters} {21} \seccontents {4.3}{GlobalParameters} {22} \seccontents {4.4}{IsDistanceRegular} {22} \seccontents {4.5}{CollapsedAdjacencyMat} {22} \seccontents {4.6}{OrbitalGraphColadjMats} {23} \seccontents {4.7}{VertexTransitiveDRGs} {23} \chapcontents {5}{Some special vertex subsets of a graph}{25} \seccontents {5.1}{ConnectedComponent} {25} \seccontents {5.2}{ConnectedComponents} {25} \seccontents {5.3}{Bicomponents} {25} \seccontents {5.4}{DistanceSet} {26} \seccontents {5.5}{Layers} {26} \seccontents {5.6}{IndependentSet} {26} \chapcontents {6}{Functions to construct new graphs from old}{27} \seccontents {6.1}{InducedSubgraph} {27} \seccontents {6.2}{DistanceSetInduced} {27} \seccontents {6.3}{DistanceGraph} {28} \seccontents {6.4}{ComplementGraph} {28} \seccontents {6.5}{PointGraph} {29} \seccontents {6.6}{EdgeGraph} {29} \seccontents {6.7}{SwitchedGraph} {30} \seccontents {6.8}{UnderlyingGraph} {30} \seccontents {6.9}{QuotientGraph} {31} \seccontents {6.10}{BipartiteDouble} {31} \seccontents {6.11}{GeodesicsGraph} {32} \seccontents {6.12}{CollapsedIndependentOrbitsGraph} {32} \seccontents {6.13}{CollapsedCompleteOrbitsGraph} {33} \seccontents {6.14}{NewGroupGraph} {34} \chapcontents {7}{Vertex-Colouring and Complete Subgraphs}{35} \seccontents {7.1}{VertexColouring} {35} \seccontents {7.2}{CompleteSubgraphs} {35} \seccontents {7.3}{CompleteSubgraphsOfGivenSize} {36} \chapcontents {8}{Automorphism groups and isomorphism testing for graphs}{38} \seccontents {8.1}{AutGroupGraph} {38} \seccontents {8.2}{IsIsomorphicGraph} {39} \seccontents {8.3}{GraphIsomorphismClassRepresentatives} {39} \seccontents {8.4}{GraphIsomorphism} {40} \chapcontents {9}{Partial Linear Spaces}{41} \seccontents {9.1}{PartialLinearSpaces} {41} \seccontents {9.2}{A research application of PartialLinearSpaces} {42} \chapcontents {}{Bibliography}{45} \chapcontents {}{Index}{46}