In Section XXXXXXXXXX, the 2-totter-free graph was introduced. Answer the following: (a) Can there exist any cycles in the 2-totter-free graph that contain vertices of the original graph? (b) Can...

In Section 4.3.2.2, the 2-totter-free graph was introduced. Answer the following:

(a) Can there exist any cycles in the 2-totter-free graph that contain vertices of the original graph?

(b) Can there exist any cycles in the 2-totter-free graph that contain vertices representing edges of the original graph?