Chapter 14 - Graph Theory - 14.1 Graphs, Paths, and Circuits - Exercise Set 14.1 - Page 902: 51

The degree of vertex A, vertex C, and vertex D is 3. Vertex B has a degree of 5. Therefore, each vertex is an odd vertex. Since each vertex is odd, this is a graph with four odd vertices and one loop at vertex B.

The degree of a vertex is the number of edges connected to the vertex. If the degree of a vertex is an odd number, then the vertex is an odd vertex. We can draw a graph with four vertices with edges AB, AC, AD, BD, CD, and BC. Then the degree of vertex A, vertex C, and vertex D is 3. Vertex B has a loop and a loop adds 2 to the degree of the vertex. Vertex B has a degree of 5. Therefore, each vertex is an odd vertex. Since each vertex is odd, this is a graph with four odd vertices and one loop at vertex B.