Consider an undirected random graph of eight vertices The probability that there is an edge between a pair of vertices is What is the expected number of unordered cycles of length three 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?

Ask Questions
GATE-Computer-Science-Engineering--Information-Technology-Question-Paper-2012-download--->View question


Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is ½. What is the expected number of unordered cycles of length three? -gate-computer science-2012

Consider an undirected random graph of eight vertices. The probability that there is an edge
between a pair of vertices is ½. What is the expected number of unordered cycles of length
three?
 (A) 1/8 (B) 1 (C) 7 (D) 8 



By:Amogh

Taged users:


Likes:
Be first to like this question

Dislikes:
Be first to dislike this question

Talk about thisDelete|Like|Dislike|


Answers

C) C
A cycle of length 3 requires 3 vertices.
Number of ways in which we can choose 3 vertices from 8 = 8C3 =56.
Probability that 3 vertices form a cycle = Probability of edge between vertices 1 and 2 * Probability of edge between vertices 2 and 3 * Probability of edge between vertices 1 and 3
=1/2 * 1/2 * 1/2 = 1/8 
So, expected number of cycles of length 3 = 56 * 1/8 = 7

milan-ransingh

Likes:
Be first to like this answer

Dislikes:
Be first to dislike this answer
Talk about this|Once you have earned teacher badge you can edit this questionDelete|Like|Dislike|
------------------------------------

Can you help us to add better answer here? Please see this



Not the answer you're looking for? Browse other questions from this Question paper or ask your own question.

Join eduladder!