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

The Correct Option is 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
\(\Rightarrow 3 n=2 \times(24)\)
\(\Rightarrow n=2 \times 8\)
\(\Rightarrow n=16\)
The sum of the degrees of all vertices in a simple graph is equal to twice the number of edges. Therefore, in this case, the sum of the degrees of all vertices is 2*24 = 48.

Since the degree of each vertex is 3, the number of vertices can be found by dividing the sum of the degrees of all vertices by the degree of each vertex, i.e., 48/3 = 16.

Therefore, the number of vertices in the graph is 16.

 

Answer 2

let n be the vertices,
Degree of each vertex =3
\(\therefore \) Total = 3n
But total degree = 2\(\times\)number of edges
= 3n : 2(24)
= n : \(\frac{2\times24}{3}\)
= n:16
So, the correct option  is (B) 16