Questions

In an undirected graph, each edge connects two vertices. Since each edge contributes 1 to the degree of each of the two vertices it connects, the total sum of the degrees of all vertices is twice the number of edges.

Explanation:

• Degree of a vertex: The degree of a vertex is the number of edges incident to that vertex.

• Sum of degrees of all vertices: Each edge in an undirected graph is counted twice—once for each of its two endpoints.

• Hence, the sum of the degrees of all vertices in the graph is 2 times the number of edges (since each edge contributes 2 to the total degree count).

Therefore, the sum of the degrees of all vertices in the graph is 2 * E.

Answer:

The correct answer is 2. 2 * E.