GATE | GATE CS 2012 | Question 36
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)
360
(B)
45
(C)
30
(D)
15
Answer: (B)
Explanation:
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)
(a, b, d, c,a)
(a, c, b, d,a)
(a, c, d, b,a)
(a, d, b, c,a)
(a, d, c, b,a)
and
(a, b, c, d,a) and (a, d, c, b,a)
(a, b, d, c,a) and (a, c, d, b,a)
(a, c, b, d,a) and (a, d, b, c,a)
are same cycles.
So total number of distinct cycles is (15*3) = 45.
Quiz of this Question
Please comment below if you find anything wrong in the above post
Last Updated :
28 Jun, 2021
Like Article
Save Article
Share your thoughts in the comments
Please Login to comment...