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A simple graph contains 24 edges. Degree of each vertex is 3 . The number of vertices is
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Verified Answer
The correct answer is:
16
Let the number of vertices $=\mathrm{n}$
Given degree of each vertex $=3$
Then, total degree of simple graph $=3 \mathrm{n}$
We know that,
$$
\begin{aligned}
&\text { sum of all degree of simple graph } \\
&\quad \begin{aligned}
\Rightarrow &=2 \times \text { number of edges in simple graph } \\
\Rightarrow \quad & \mathrm{n}=2 \times(24) \\
\Rightarrow \quad \mathrm{n} &=2 \times 8 \\
\Rightarrow \quad \mathrm{n} &=16
\end{aligned}
\end{aligned}
$$
Given degree of each vertex $=3$
Then, total degree of simple graph $=3 \mathrm{n}$
We know that,
$$
\begin{aligned}
&\text { sum of all degree of simple graph } \\
&\quad \begin{aligned}
\Rightarrow &=2 \times \text { number of edges in simple graph } \\
\Rightarrow \quad & \mathrm{n}=2 \times(24) \\
\Rightarrow \quad \mathrm{n} &=2 \times 8 \\
\Rightarrow \quad \mathrm{n} &=16
\end{aligned}
\end{aligned}
$$
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