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 gate computer science 2012

The Eduladder is a community of students, teachers, and programmers just interested to make you pass any exams. So we solve previous year question papers for you.
See Our team
Wondering how we keep quality?
Got unsolved questions?

## 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 -gate-computer science-2012

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) 360

Taged users:

Likes:
Be first to like this question

Dislikes:
Be first to dislike this question

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.

Likes:
Be first to like this answer

Dislikes:
Be first to dislike this answer

You may also like our videos

Below are some of the videos from our collection. We saw that students not only needed content but also videos. So, we decided to build a video platform for you also an algorithm which shows best videos suites to you related to the content you are browsing check out some videos which suit best for you.

Lets together make the web is a better place

We made eduladder by keeping the ideology of building a supermarket of all the educational material available under one roof. We are doing it with the help of individual contributors like you, interns and employees. So the resources you are looking for can be easily available and accessible also with the freedom of remix reuse and reshare our content under the terms of creative commons license with attribution required close.

You can also contribute to our vision of "Helping student to pass any exams" with these.