OddGraph[n] returns the graph whose vertices are the size-(n - 1) subsets of a size-(2 nTraditionalForm\`\[Dash]1) set and whose edges connect pairs of vertices that ...

Partitions[n] constructs all partitions of integer n in reverse lexicographic order. Partitions[n, k] constructs all partitions of the integer n with maximum part at most k, ...

PerfectQ[g] yields True if g is a perfect graph, meaning that for every induced subgraph of g the size of a largest clique equals the chromatic number.

PermuteSubgraph[g, p] permutes the vertices of a subgraph of g induced by p according to p.

RandomKSetPartition[set, k] returns a random set partition of set with k blocks. RandomKSetPartition[n, k] returns a random set partition of the first n natural numbers into ...

RandomSetPartition[set] returns a random set partition of set. RandomSetPartition[n] returns a random set partition of the first n natural numbers.

RootedEmbedding[g, v] constructs a rooted embedding of graph g with vertex v as the root. RootedEmbedding[g] constructs a rooted embedding with a center of g as the root.

SetPartitionQ[sp, s] determines if sp is a set partition of set s. SetPartitionQ[sp] tests if sp is a set of disjoint sets.

ShakeGraph[g, d] performs a random perturbation of the vertices of graph g, with each vertex moving, at most, a distance d from its original position.

ShowGraphArray[{g_1, g_2, ...}] displays a row of graphs. ShowGraphArray[{{g_1, ...}, {g_2, ...}, \ ...}] displays a two-dimensional table of graphs.