Question

A simple graph contains $24$ edges. Degree of each vertex is $3$. The number of vertices is .................

• A. 21
• B. 16
• C. 8
• D. 12

Answer 1

Answer: (B)

Let the number of vertices $=n$
Given degree of each vertex $=3$
Then, total degree of simple graph $=3 n$
We know that,
sum of all degree of simple graph
$=2 \times$ number of edges in simple graph
$\Rightarrow 3 n=2 \times(24)$
$\Rightarrow n=2 \times 8$
$\Rightarrow n=16$