KCET · Maths · Basic of Mathematics
A simple graph contains 24 edges. Degree of each vertex is 3 . The number of vertices is
- A 8
- B 12
- C 21
- D 16
Answer & Solution
Correct Answer
(D) 16
Step-by-step Solution
Detailed explanation
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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