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

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

Tardigrade Admin · Accepted Answer

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 × number of edges in simple graph ⇒ 3 n=2 ×(24) ⇒ n=2 × 8 ⇒ n=16

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

21

16

8

12

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
$\Rightarrow 3 n = 2 \times (24)$
$\Rightarrow n = 2 \times 8$
$\Rightarrow n = 16$

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

21

16

8

12

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

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

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
$\Rightarrow 3 n = 2 \times (24)$
$\Rightarrow n = 2 \times 8$
$\Rightarrow n = 16$