Exercises 7–12 can be done as homework problems or in-class activities.
7. Draw a graph with four vertices in which:
a. each vertex is of degree 2.
b. each vertex is of degree 3.
c. two vertices are of degree 2 and two are of degree 3.
8. Draw a graph with five vertices in which:
a. each vertex is of degree 2.
b. each vertex is of degree 4.
c. one vertex is of degree 2 and four are of degree 3.
9. Draw a graph with six vertices in which:
a. each vertex is of degree 1.
b. each vertex is of degree 0.
10. Draw a graph with eight vertices in which each vertex is of degree 3.
11. Draw a graph with six vertices in which each vertex is of degree 3 and that has:
a. loops but no multiple edges.
b. multiple edges but no loops.
c. neither loops nor multiple edges.
d. both loops and multiple edges.
12. Draw a graph with five vertices in which each vertex is of degree 4 and that has:
a. loops but no multiple edges.
b. multiple edges but no loops.
c. neither loops nor multiple edges.
d. both loops and multiple edges.