VertexList[g] gives the list of vertices for the graph g.VertexList[g, patt] gives a list of vertices that match the pattern patt.
EdgeList[g] gives the list of edges for the graph g. EdgeList[g, patt] gives a list of edges that match the pattern patt.
IsomorphicGraphQ[g_1, g_2] yields True if the graphs g_1 and g_2 are isomorphic, and False otherwise.
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CayleyGraph[group] returns a Cayley graph representation of group.
UndirectedGraph[g] gives an undirected graph from the directed graph g.
TuranGraph[n, k] gives the k-partite TurĂ¡n graph with n vertices T n, k.
FindGraphIsomorphism[g_1, g_2] finds an isomorphism that maps the graph g_1 to g_2 by renaming vertices.
AcyclicGraphQ[g] yields True if the graph g is an acyclic graph and False otherwise.
DirectedGraph[g] gives a directed graph from the undirected graph g.DirectedGraph[g, conv] gives a directed graph using the conversion conv.