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

To find the number of distinct cycles of length 4 in a complete labeled graph $K_6$:

1. Choose 4 vertices out of the 6 vertices:

   $$\binom{6}{4} = 15$$

2. The number of distinct undirected cycles that can be formed using a specific set of 4 labeled vertices is:

   $$\frac{(4 - 1)!}{2} = \frac{3!}{2} = \frac{6}{2} = 3$$

3. Therefore, the total number of distinct 4-cycles in $K_6$ is:

   $$15 \times 3 = 45$$

Since 45 was not present among the given options (15, 30, 90, 360), marks were awarded to all candidates (Marks to All in the official key).