Question

7. A graph has six vertices: two vertices of degree 5, two vertices of degree 3, and two vertices of degree 4. What is the number of edges in the graph? a) 6 b) 12 c) 24 d) 48 e) None of the above.

Answer 1

Ok so you have:

Two vertices of degree 5

Two vertices of degree 3

Two vertices of degree 4

Now, calculate the sum of the degrees:

Sum of degrees = (2 * 5) + (2 * 3) + (2 * 4) = 10 + 6 + 8 = 24

Now, use the Handshaking Lemma to find the number of edges:

2 * (number of edges) = 24

Divide both sides by 2:

(number of edges) = 24 / 2 = 12

So, the number of edges in the graph is 12. Therefore, the correct answer is (b) 12.