Uttrakhand Asst. Professor Exam-37

Question

A complete graph with 15 vertices has ____ edges

• A. 15
• B. 120
• C. 105
• D. 210

Answer 1

In a complete graph , a vertex should have edges with all other vertices. 

A complete graph with n-vertices is denoted by K_{n ,} where each vertex has degree (n-1)

& the sum of all degrees is n * (n-1).

Now, the handshaking theorem tell us that , the number of edges in K_n would be $\dfrac{{n}*{(n-1)}}{2}$ edges.

If the number of vertices is 15 , number of edges will  be $\dfrac{{15}*{(15-1)}}{2}$ = $15 * 7$ =105 

Answer 2

Complete  Graph if 'n' is the number of nodes and 'E' is the number of edges.

E = $\frac{(n)(n-1)}{2}$

put n = 15

E = $\frac{(15)(15-1)}{2}$

E = $\frac{(15)(14)}{2}$

E = 15 * 7

E = 105

So,answer is (C)