Consider a simple undirected graph with 6 vertices. The degrees of the vertices in this graph are as follows: vertex A has degree 3, vertex B has degree 2, vertex C has degree 4, vertex D has degree 3, vertex E has degree 3, and vertex F has degree 1. Calculate the number of edges in the graph.a.6b.7c.8d.12

The number of edges in an undirected graph can be calculated by summing the degrees of all vertices and then dividing by 2. This is because each edge is connected to two vertices and thus contributes to the degree of two vertices.

Here are the steps to calculate the number of edges:

1. Sum the degrees of all vertices: 3 (A) + 2 (B) + 4 (C) + 3 (D) + 3 (E) + 1 (F) = 16
2. Divide the sum by 2: 16 / 2 = 8

So, the graph has 8 edges. The correct answer is c. 8.

To calculate 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 an undirected graph is equal to twice the number of edges.

In this case, the sum of the degrees of all vertices is 3 + 2 + 4 + 3 + 3 + 1 = 16.

According to the Handshaking Lemma, the number of edges in the graph is equal to half of the sum of the degrees, which is 16/2 = 8.

Therefore, the correct answer is c. 8.

The number of edges in an undirected graph can be calculated by summing the degrees of all vertices and then dividing by 2. This is because each edge is connected to two vertices, and thus each edge is counted twice when summing the degrees of the vertices.

Here are the steps to calculate the number of edges:

1. Sum the degrees of all vertices: 3 (A) + 2 (B) + 4 (C) + 3 (D) + 3 (E) + 1 (F) = 16
2. Divide the sum by 2: 16 / 2 = 8

So, the graph has 8 edges. The correct answer is c.8.