GraphPower[g, k] gives the k\[Null]^th power of graph g. This is the graph whose vertex set is identical to the vertex set of g and that contains an edge between vertices i ...

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.

HamiltonianQ[g] yields True if there exists a Hamiltonian cycle in graph g, or in other words, if there exists a cycle that visits each vertex exactly once.

HerschelGraph returns a graph object that represents a Herschel graph.

HighlightedEdgeColors is an option to Highlight that determines which colors are used for the highlighted edges.

HighlightedEdgeStyle is an option to Highlight that determines how the highlighted edges are drawn.

HighlightedVertexColors is an option to Highlight that determines which colors are used for the highlighted vertices.

HighlightedVertexStyle is an option to Highlight that determines how the highlighted vertices are drawn.

Highlight[g, p] displays g with elements in p highlighted. The second argument p has the form {s_1, s_2, ...}, where the s_i are disjoint subsets of vertices and edges of g.