Question

find the smallest n such that the complete graph Kn has atleast 600 edges.​

Answer 1

Answer:

36

Step-by-step explanation:

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Answer 2

The smallest value of n = 36 such that the complete graph Kₙ has atleast 600 edges.

Given :

The complete graph Kₙ has atleast 600 edges

To find :

The smallest value of n

Solution :

Step 1 of 2 :

Form the inequality to find the value of n

We know that a complete graph Kₙ has n(n - 1)/2 edges

By the given condition

$\displaystyle \sf{ \frac{n(n - 1)}{2} \geqslant 600 }$

Step 2 of 2 :

Find the smallest value of n

$\displaystyle \sf{ \frac{n(n - 1)}{2} \geqslant 600 }$

$\displaystyle \sf{ \implies n(n - 1) \geqslant 1200}$

Now

35 × 34 = 1190 < 1200

36 × 35 = 1260 > 1200

Hence the required smallest value of n = 36