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Computer Science (GATE Exam) 2013 - Previous Question Paper Solution
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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?
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A
7
💡 Explanation:
P(edge) $ = \dfrac{1}{2}$
Number of ways we can choose the vertices out of 8 is $^8C_2$.
(Three edges in each cycle)
Expected number of unordered cycles of length 3 =$^8C_2$$ \times \left( \dfrac{1}{2} \right)^3$