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GATE Overflow Test Series | Discrete Mathematics | Test 4 | Question: 7

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Let the total number of vertices be $n$.

Using sum of the degrees theorem:$5\times 6 + (n-5)\times 5 = 2e = 90$

$\implies 30+5(n-5)=90$

$\implies n = 17$

So, the correct answer is $17$.
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