12,514 views

## 9 Answers

0 votes

no of vertices =n

min degree for each vertex =3

now total degree =3*n

no of edge =25

now we know for undirected graph ,

2*edge = sum of degree

sum of degree =2*25 =50

now 3*n = 50

n= 16.67

now if someone confused which one to took ceil of floor

now just think if we put n= 17 then 3*17 =51 which is not the sum of degree as it is 50 and we can’t say 16 vertex of degree 3 and one vertex of degree 2 as min degree should be 3.

now if you choose 16 then 16*3 =48 which is also not equal to 50 also but here is the possibility that we have 15 vertex of degree 3 and one vertex of degree 5 as 5 is greater than min degree 3 .so ,3*15 +5 =50 .

thats why we took 16 as answer.

min degree for each vertex =3

now total degree =3*n

no of edge =25

now we know for undirected graph ,

2*edge = sum of degree

sum of degree =2*25 =50

now 3*n = 50

n= 16.67

now if someone confused which one to took ceil of floor

now just think if we put n= 17 then 3*17 =51 which is not the sum of degree as it is 50 and we can’t say 16 vertex of degree 3 and one vertex of degree 2 as min degree should be 3.

now if you choose 16 then 16*3 =48 which is also not equal to 50 also but here is the possibility that we have 15 vertex of degree 3 and one vertex of degree 5 as 5 is greater than min degree 3 .so ,3*15 +5 =50 .

thats why we took 16 as answer.

–3 votes

## Ans : 17

## Sum of Degrees of Vertices Theorem

If G = (V, E) be a non-directed graph with vertices V = {V_{1}, V_{2},…V_{n}} then

n∑i=1 deg(V_{i}) = 2|E|

If the answer is 16 i.e. 16 Vertices of which degree of each vertex is 3 then Sum of degree of all the vertices is 48 but according to Sum of degree of Vertices therom it should be 2*25= 50. Hence, the answer should be 17.