How can I find all the acyclic orientations of a kite?
Try:
I found out the 6 orientations for $K_{3}$ but I don't know what to do in the case of kite as there 2 triangles attached one in upward direction and other in downward. In $K_{3}$ 6 out of 8 were not giving an orientated circuit so that's why there were 6 acyclic orientations nut how to do that in this case
I even found out that there will be 6 acycylic orientations with the help of chromatic polynomial. Just having a tough time in drawing them
Any help will be appreciated
The chromatic polynomial is n(n-1)(n-2)^2. So there are actually 18 acyclic directed graphs not 6 (this number comes from plugging in -1 for n and taking the absolute value. Find them by drawing 18 kites then adding an orientation to each edge making sure that there are no cycles.