Are ordered pairs (V, E) where

[A bag is like a set but elements can be repeated]

Arrows show direction on a directed graph.

Directed graphs are ordered pairs where

Every vertex is connected to every other vertex.

A graph is connected if every pair of vertices v,w can be connected by a path which starts at v and ends at w

A path in a graph is a sequence of oriented edges such that the end point of one oriented edge is the beginning of the next.

A circuit is a path that starts and ends at the same point.

A tree is a connected, undirected simple graph with no cycles.

Select one vertex and orient all edges to form a directed path from the root to all other vertices.

A vertex with no children.

A vertex with children.

Vertices between the current vertex and the root.

Vertices between the current vertex and the end of the tree.

[ ^{n}P_{r} = frac{n!}{(n-r)!} hspace{10 mm} ^{n}C_{r} = frac{n!}{r!(n-r)!} ]

There exists two constants and such that for , .

[ sum_{i=1}^{n} i = 1 + 2 + 3 + … + n = { n(n+1) over 2 } ]