Discrete Mathematics

A complete graph with n vertices (denoted by K_n) in which each vertex is connected to each of the others (with one edge between each pair of vertices).
Steps to draw a complete graph:

• First set how many vertexes in your graph. Say 'n' vertices, then the degree of each vertex is given by 'n – 1' degree. i.e.
  degree of each vertex = n – 1
• Find the number of edges, if the number of vertices areas in step 1. i.e.
  Number of edges = n(n-1)/2
• Draw the complete graph of above values.

Some figures of complete graphs for number of vertices for n = 1 to n = 7.
The complete Graph when
number of vertex is 1, its degree of a vertex = n – 1 = 1 – 1 = 0, and number of edges = n(n – 1)/2 = 1(1-1)/2 = 0

Complete Graph (K1)
number of vertex is 2, its degree of a vertex = n – 1 = 2 – 1 = 1, and number of edges = n(n – 1)/2 = 2(2-1)/2 = 1

Complete Graph (K2)
number of vertex is 3, its degree of a vertex = n – 1 = 3 – 1 = 2, and number of edges = n(n – 1)/2 = 3(3-1)/2 =3

Complete Graph (K3)
number of vertex is 4, its degree of a vertex = n – 1 = 4 – 1 = 3, and number of edges = n(n – 1)/2 = 4(4-1)/2 =6

Complete Graph (K4)
number of vertex is 5, its degree of a vertex = n – 1 = 5 – 1 = 4, and number of edges = n(n – 1)/2 = 5(5-1)/2 =10

Complete Graph (K5)
number of vertex is 6, its degree of a vertex = n – 1 = 6 – 1 = 5, and number of edges = n(n – 1)/2 = 6(6 – 1)/2 = 15

Complete Graph (K6)
number of vertex is 7, its degree of a vertex = n – 1 = 7 – 1 = 6, number of edges = n(n – 1)/2 = 7(7 – 1)/2 = 21

Complete Graph (K7)