(a) Let (6, 5, 4, 3, 2, 1, ..., 1) be the graph score of a tree. How many 1's are there in the sequence?  

(b) Show that if T is a tree containing at least one vertex of degree 2 then the complement of T is not Eulerian.

(c) Prove or disprove: Let (T, r, ) and (T, r, ) be planted trees. If (T, r) and (T, r) are isomorphic as rooted trees then (T, r, ) are (T, r, ) isomorphic as planted trees.