Mathematica has been used to make many important discoveries in discrete mathematics over the past two decades. Its integration of highly efficient and often original algorithms together with its high-level symbolic language has made it a unique environment for the exploration, development, and application of discrete mathematics.
RSolve — solve recurrence equations
FindSequenceFunction — find functions for integer sequences
ReplaceList — generate a list of forms matching a pattern
TreePlot — display trees
GraphData — database of named and enumerated graphs and their properties
FindShortestTour — solve traveling salesman problems