Chapter 14 - Graph Theory - Chapter Summary, Review, and Test - Review Exercises - Page 935: 3

The odd vertices are vertex A and vertex C. The even vertices are vertex B, vertex, D, and vertex E.

The degree of a vertex is the number of edges connected to that vertex. If the degree of a vertex is an even number, then the vertex is an even vertex. If the degree of a vertex is an odd number, then the vertex is an odd vertex. Vertex A has 3 edges connecting it to other vertices. Vertex A also has a loop which adds 2 to the degree of the vertex. Therefore, the degree of vertex A is 5. Vertex A is an odd vertex. Vertex B has 4 edges connected to it, so the degree of vertex B is 4. Vertex B is an even vertex. Vertex C has 5 edges connected to it, so the degree of vertex C is 5. Vertex C is an odd vertex. Vertex D has 4 edges connected to it, so the degree of vertex D is 4. Vertex D is an even vertex. Vertex E has 2 edges connected to it, so the degree of vertex E is 2. Vertex E is an even vertex.