To determine the degree of vertex $E$ in the graph shown in the image:

The degree of a vertex in a graph is the number of edges connected to it.

From the graph:

• Vertex $E$ is connected to $D$, $F$, and $C$.

Thus, the degree of vertex $E$ is 3.

Would you like more details about graph theory or degrees of vertices?

Here are 5 related questions for exploration:

1. What is the degree of vertex $D$ in this graph?
2. How do we classify graphs based on degrees of vertices (e.g., regular graphs)?
3. Can the sum of all vertex degrees in a graph indicate the number of edges?
4. What is the difference between an undirected and a directed graph in terms of vertex degrees?
5. How does the concept of degree apply in weighted graphs?

Tip: Remember, in undirected graphs, each edge contributes 1 to the degree of each connected vertex.