Examples for

Graph Theory

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.

Named Graphs

Refer to common graphs by their names. Look up their properties or use them in comparisons and computations.

Compute properties of a named graph:

Specify graphs with symbolic parameters:

Compare several graphs:

Get a graph polynomial:

Random Graphs

Generate random graphs with certain numbers of vertices and edges.

Create a random graph with a fixed number of vertices:

Specify the number of vertices and edges:

Adjacency Rules

Construct graphs by specifying their adjacency lists, look up a known graph's adjacency list or find paths and cycles.

Analyze a graph specified by adjacency rules:

Compute an Eulerian cycle:

Regular Trees

Compute properties of k-ary trees, graphs that are acyclic and with vertices of degree 1 or k.

Compute properties of a regular k-ary tree:

Specify the number of levels:

More examples