A counterexample to a conjecture of Ghosh
  We answer two questions of Shamik Ghosh in the negative. We show that there exists a lobster tree of diameter less than 6 which accepts no alpha-labeling with two central vertices labeled by the critical number and the maximum vertex label. We also show a simple example of a tree of diameter 4, with an even degree central vertex which does not accept a maximum label in any graceful labeling. 
Hung Hua, Elliot Krop, and Christopher Raridan
math.CO