A counterexample to a conjecture of Ghosh
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Authors
Elliot Krop
Christopher Raridan
Hung Hua
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Journal Article, Academic Journal
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Abstract
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 observe that this simple example is a tree of diameter 4 with an even degree central vertex which does not accept a maximum label in any graceful labeling.