GraphSum[g_1, g_2, ...] constructs the graph resulting from joining the edge lists of graphs g_1, g_2, and so forth.

GraphUnion[g_1, g_2, ...] constructs the union of graphs g_1, g_2, and so forth. GraphUnion[n, g] constructs n copies of graph g, for any nonnegative integer n.

GrayCodeKSubsets[l, k] generates k-subsets of l in Gray code order.

GrayCodeSubsets[l] constructs a binary reflected Gray code on set l.

GrayGraph returns a 3-regular, 54-vertex graph that is edge-transitive but not vertex-transitive\[LongDash]the smallest known such example.

Greedy is a value that the option Algorithm can take in calls to functions such as VertexCover, telling the function to use a greedy algorithm.

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 ...

GridGraph[n, m] constructs an n*m grid graph, the product of paths on n and m vertices. GridGraph[p, q, r] constructs a p*q*r grid graph, the product of GridGraph[p, q] and a ...

GroetzschGraph returns the smallest triangle-free graph with chromatic number 4. This is identical to MycielskiGraph[4].

HamiltonianCycle[g] finds a Hamiltonian cycle in graph g if one exists. HamiltonianCycle[g, All] gives all Hamiltonian cycles of graph g.