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Maximum number of edges in a n - node undirected graph without self loops is
  • a)
    n2
  • b)
    n(n - 1)/2
  • c)
    n - 1
  • d)
    (n + 1) (n)/2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Maximum number of edges in a n - node undirected graph without self lo...
Background required - Basic Combinatorics Since the given graph is undirected, that means the order of edges doesn't matter. Since we have to insert an edge between all possible pair of vertices, therefore problem reduces to finding the count of the number of subsets of size 2 chosen from the set of vertices. Since the set of vertices has size n, the number of such subsets is given by the binomial coefficient C(n,2) (also known as "n choose 2"). Using the formula for binomial coefficients, C(n,2) = n(n-1)/2.
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Maximum number of edges in a n - node undirected graph without self loops isa)n2b)n(n - 1)/2c)n - 1d)(n + 1) (n)/2Correct answer is option 'B'. Can you explain this answer?
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