Graph theory is the branch of mathematics dedicated to studying structures made up of vertices connected by directed or undirected edges. Wolfram|Alpha has a variety of functionality relating to graphs. Look up known graphs, generate graphs from adjacency lists or compute properties of graphs, such as the chromatic number.
Refer to common graphs by their names. Look up their properties or use them in comparisons and computations.
Generate random graphs with certain numbers of vertices and edges.
Construct graphs by specifying their adjacency lists, look up a known graph's adjacency list or find paths and cycles.
Compute properties of k-ary trees, graphs that are acyclic and with vertices of degree 1 or k.