Let G be a complete undirected graph on 6 vertices. If vertices of G are labeled, then the number of distinct cycles of length

4 in G is equal to

A. 15

B. 30

C. 90

D. 45

# Graph Theory DM

**Ruturaj**#4

6C4 is the number of ways we can choose 4 vertices out of 6 vertices.

Now (4-1)!/2 is the number of ways we can arrange those 4 vertices. As they are in a circular closed path so we have to fix one node and permute the others. Thatâ€™s why (4-1)!. and as both clock wise and anticlockwise would be same for a garland if reversed, so divided by 2.