an:06568493
Zbl 1334.05143
Hua, Hung; Krop, Elliot; Raridan, Christopher
A counterexample to a conjecture of Ghosh
EN
Bull. Inst. Comb. Appl. 75, 79-82 (2015).
00350698
2015
j
05C78
graceful labeling; graceful tree conjecture; Bermond's conjecture; lobster
Summary: We answer two questions of \textit{S. Ghosh} [``On certain classes of graceful lobsters'', Preprint, \url{arXiv:1306.2932}] 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.