Graph Theory
A few examples of what you can ask Wolfram|Alpha about:
Named Graphs
compute properties of a named graph
specify graphs with symbolic parameters
compare several graphs
get a graph polynomial
Adjacency Rules
analyze a graph specified by adjacency rules
compute an Eulerian cycle
Random Graphs
create a random graph with a fixed number of vertices
specify number of vertices and edges
compute properties of a regular k-ary tree
specify the number of levels