OctahedralGraph returns the graph corresponding to the octahedron, a Platonic solid.

RandomVertices[g] assigns a random embedding to graph g.

TetrahedralGraph returns the graph corresponding to the tetrahedron, a Platonic solid.

WaltherGraph returns the Walther graph.

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AntiSymmetricQ[g] yields True if the adjacency matrix of g represents an anti-symmetric binary relation.

BrelazColoring[g] returns a vertex coloring in which vertices are greedily colored with the smallest available color in decreasing order of vertex degree.

DominatingIntegerPartitionQ[a, b] yields True if integer partition a dominates integer partition b, that is, the sum of a size-t prefix of a is no smaller than the sum of a ...

Neighborhood[g, v, k] returns the subset of vertices in g that are at a distance of k or less from vertex v. Neighborhood[al, v, k] behaves identically, except that it takes ...

ParentsToPaths[l, i, j] takes a list of parents l and returns the path from i to j encoded in the parent list. ParentsToPaths[l, i] returns the paths from i to all vertices.