1.3 Vertex degrees and counting
    Degree sequences and graphic sequences.
      d1 >= ... >= dn is a degree sequence of some graph
      if and only if their sum is even.
      A graphic sequence is a degree sequence of a simple graph,
        for which we saw an algorithmic test.
      2-switches maintain the degree sequence of a graph
1.4  Digraphs
    The underlying graph is the undirected version
    Weakly connected versus strongly connected
    Vertex indegrees and outdegrees
        sum of indegrees = sum of outdegrees
    Eulerian digraphs
        A digraph is Eulerian if and only if indegree=outdegree
        at every node.  Application to de Bruijn cycles.
    Tournaments are orientations of the clique

2.1 Trees and distance
    Forest, tree, leaf, spanning tree
    Four equivalent definitions of a tree
    Given two spanning trees T and T' there are two theorems about
        taking an edge from one to replace an edge in the other and
        get another spanning tree.
    Distance, diameter, eccentricity, radius, center
2.2 Spanning trees and Enumeration (1st section only)
    Cayley's formula:  there are n^(n-2) labeled trees on n vertices
        Proof using Prufer codes
2.3 Optimization and Trees
    Kruskal's algorithm for minimum spanning tree
    Dijkstra's algorithm for single-source shortest paths