A graph G = (V,E) consists of two sets V and E. The elements of V are called vertices while that of E are called edges. Each edge e is associated with an unordered pair vi,vj of vertices
An edge having the same vertex at both ends is called a loop.
Two edges associated with the same pair of end vertices are called parallel edges.
A graph which does not contain loops or parallel edges is called a simple graph.
The number of edges incident on a vertex v with loops being counted twice is called the degree of the vertex v.
A graph in which all vertices are of equal degree is called a regular graph.
A vertex having no incident edge is called an isolated vertex.
graph having no edges is called a null graph.
Theorem 1 :
The sum of the degrees of all vertices of a graph is equal to twice the number of edges of the graph.
Theorem 2 :
A graph always contains a even number of vertices of odd degree.