Degrees — list of degrees of vertices
DegreeSequence — list number of edges for each vertex
GraphicQ — test if a list of integers is a graphic sequence
ListGraphs — list of nonisomorphic undirected graphs
NumberOfGraphs — number of nonisomorphic undirected graphs with
n vertices
ConnectedComponents — get lists of connected components
TwoColoring — color vertices of a bipartite graph
ChromaticPolynomial — compute chromatic polynomial for a graph
ChromaticNumber — smallest number of colors to color the graph
MinimumVertexColoring — color a graph with the fewest colors
IsomorphicQ — test if two graphs are isomorphic
PseudographQ — test if a graph is a pseudograph
AcyclicQ — test if a graph is acyclic
