GraphDifference[g, h] constructs the graph resulting from subtracting the edges of graph h from the edges of graph g.

GraphicQ[s] yields True if the list of integers s is a graphic sequence, and thus represents a degree sequence of some graph.

GraphIntersection[g_1, g_2, ...] constructs the graph defined by the edges that are in all the graphs g_1, g_2, ....

GraphProduct[g_1, g_2, ...] constructs the product of graphs g_1, g_2, and so forth.

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

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

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

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 ...

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

HamiltonianPath[g] finds a Hamiltonian path in graph g if one exists. HamiltonianPath[g, All] gives all Hamiltonian paths of graph g.