What is the maximum number of edges that can be present in a simple undirected graph with N vertices?

Options

  • A. N-1
  • B. N
  • C. N(N-1)/2
  • D. More than one of the above
  • E. None of the above

Correct Answer (Detailed Explanation is Below)

C. N(N-1)/2

Detailed Explanation

In a simple undirected graph, there can be at most one edge between any pair of distinct vertices and no self-loops. The number of possible vertex pairs is N(N - 1)/2, so this is the maximum number of edges. This should not be confused with a tree, which has exactly N - 1 edges. A complete graph KN achieves this maximum.

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