Complete graph has n vertices then what will be the no of edges

Q.  If a complete graph has n vertices then what will be the no of edges?
- Published on 23 Jun 15

a. n-1
b. (n-1)/2
c. (1/2) n (n-1)
d. None of the above.

ANSWER: (1/2) n (n-1)

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    Discussion

  • Nihal   -Posted on 01 Apr 16
    A complete graph is a graph in which each pair of graph vertices is connected by an edge. If a complete graph has 'n' vertices then the no. of edges will be (1/2) n (n-1). It is denoted by Kn.

    Properties of complete graph:
    • It is a loop free and undirected graph.
    • Each vertex has degree N-1
    • The sum of all degrees is N (N-1)
    Example: Suppose the number of vertices in complete graph is 15 then the number of edges will be (1/2)15 * 14 = 105

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