Chapter 14 - Graph Theory - 14.1 Graphs, Paths, and Circuits - Exercise Set 14.1 - Page 901: 23

The degree of vertex A is 2. The degree of vertex B is 2. The degree of vertex C is 3. The degree of vertex D is 3. The degree of vertex E is 3. The degree of vertex F is 1.

The degree of a vertex is the number of edges connected to that vertex. Vertex A has 2 edges connected to it, so the degree of vertex A is 2. Vertex B has 2 edges connected to it, so the degree of vertex B is 2. Vertex C has 3 edges connected to it, so the degree of vertex C is 3. Vertex D has 3 edges connected to it, so the degree of vertex D is 3. Vertex E has 1 edge connecting it to vertex D. Vertex E also has a loop which adds 2 to the degree of the vertex. Therefore, the degree of vertex E is 3. Vertex F has 1 edge connected to it, so the degree of vertex F is 1.