Graph Theory
A graph is a set of objects called vertices (or nodes) connected by links called edges .
A finite simple graph is an ordered pair G = [ V , E ] , where V is a finite set of vertices or nodes and each element of E is a 2-element subset of V . Typically, a graph is depicted as a set of dots (the vertices) connected by lines (the edges).
The order of a graph is | V | (the number of vertices). A graph's size is | E | , the number of edges. The degree of a vertex is the number of edges that connect to it.
Example:
In the above graph, the set of vertices are 
and the set of edges are 
.
The order of the graph is .
The size of the graph is .
The number of edges that connect with vertex u is 2 and therefore the degree of the vertex u is 2.
Vertices |
Degree |
u |
2 |
v |
3 |
w |
2 |
r |
3 |
s |
2 |
