Because the five vertices of K5 are symmetrical, isomorphism is only related to the degree of the new vertex. The minimum angle of the new vertex is 2 degrees and the maximum angle is 5 degrees. So there are four different structures.

Question 2: 9

In K3,3, the three vertices on the left are equivalent, and the three vertices on the right are equivalent. So isomorphism is only related to how many sides are added to the left and right. Because of the left-right symmetry, we only consider the case that the number of edges on the left is greater than that on the right. A * * * there are nine possibilities:

(1) Add 1 edge to the left and 0 edge to the right;

(2) Add 2 sides to the left and 0 sides to the right;

(3) Add 1 edge to the left and 1 edge to the right;

(4) Add 3 sides to the left and 0 sides to the right;

(5) Add 2 edges to the left and 1 edge to the right;

(6) Add 3 edges to the left and 1 edge to the right;

(7) Add 2 sides to the left and 2 sides to the right;

(8) Add 3 sides on the left and 2 sides on the right;

(9) Add 3 sides to the left and 3 sides to the right;