GreedyVertexCover[g] returns a vertex cover of graph g constructed using the greedy algorithm. This is a natural heuristic for constructing a vertex cover, but it can produce ...

KnightsTourGraph[m, n] returns a graph with mn vertices in which each vertex represents a square in an m*n chessboard and each edge corresponds to a legal move by a knight ...

MaximumClique[g] finds a largest clique in graph g. MaximumClique[g, k] returns a k-clique, if such a thing exists in g; otherwise it returns {}.

MeredithGraph returns a 4-regular, 4-connected graph that is not Hamiltonian, providing a counterexample to a conjecture by C. St. J. A. Nash\[Dash]Williams.

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.

RotateVertices[v, \[Theta]] rotates each vertex position in list v by \[Theta] radians about the origin (0, 0). RotateVertices[g, \[Theta]] rotates the embedding of the graph ...

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.

TranslateVertices[v, {x, y}] adds the vector {x, y} to the vertex embedding location of each vertex in list v. TranslateVertices[g, {x, y}] translates the embedding of the ...

VertexColor is an option that allows the user to associate colors with vertices.

VertexLabelColor is an option that allows the user to associate different colors to vertex labels.