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:

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