Answer to Question #216193 in Discrete Mathematics for Wavie

Question

Question 5. A graph has 24 edges, 4 vertices of degree 5, and all other vertices of degree 2.

How many nodes does it have in total?

Answer 1

Solution

There are 4 nodes(vertices) of degree 5.

Let x be number of nodes of degree 2.

Total number of nodes will be x+4.

But

2(number of edges)=sum of degrees

2(24)=5(4)+2(x)

48=20+2x

x=14

Total number of nodes:

x+4=14+4=18

Answer:

18 nodes