A graph has 6 vertices, and each vertex has a degree of 2 except for one vertex, which has a degree of 4. Determine the number of edges in the graph.a.4b.7c.12d.16

The degree of a vertex in a graph is the number of edges connected to it. The sum of the degrees of all vertices in a graph is equal to twice the number of edges (since each edge is connected to two vertices).

In this graph, we have 5 vertices each with a degree of 2 and 1 vertex with a degree of 4. So, the sum of the degrees of all vertices is 5*2 + 4 = 14.

Since the sum of the degrees of all vertices is equal to twice the number of edges, we can find the number of edges by dividing the sum of the degrees by 2.

So, the number of edges in the graph is 14 / 2 = 7.

Therefore, the correct answer is b.7.

To determine the number of edges in the graph, we can use the Handshaking Lemma, which states that the sum of the degrees of all vertices in a graph is equal to twice the number of edges.

Given that there are 6 vertices in the graph, and each vertex has a degree of 2 except for one vertex with a degree of 4, we can calculate the sum of the degrees as follows:

(5 vertices with a degree of 2) * 2 + (1 vertex with a degree of 4) = 10 + 4 = 14

According to the Handshaking Lemma, this sum is equal to twice the number of edges. Therefore, we can divide the sum by 2 to find the number of edges:

14 / 2 = 7

Therefore, the correct answer is option b.7.