Question

Q4. G is a complete graph on 6 vertices. If vertices of G are labelled with 1, 2, 3, 4, 5, 6, find the number of distinct cycles of length 6 in G.​

Answer 1

Answer:

There can be total 6C4 ways to pick 4 vertices from 6. The value of 6C4 is 15.

Note that the given graph is complete so any 4 vertices can form a cycle.

There can be 6 different cycle with 4 vertices. For example, consider 4 vertices as a, b, c and d. The three distinct cycles are

cycles should be like this

(a, b, c, d,a)