The handshaking Theorem
Theorem: Let G=(V,E) be an undirected graph with k edges. Then
Corollary: An undirected graph has an even number of vertices
In a directed graph, the in-degree of a vertex v, denoted by deg-(v), is
number of edges with v as their terminal vertex.
The outdegree of v, denoted by deg+(v), is is the number of edges with
v as their initial vertex.
Theorem. Let G=(V,E) be a directed graph. Then
? deg-(v) = ? deg+(v) = |E|.