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Published in:
2011 | OriginalPaper | Chapter
On Graceful Labelings of Trees
(Extended Abstract)
Authors : Sourabh Aryabhatta, Tonmoy Guha Roy, Md. Mohsin Uddin, Md. Saidur Rahman
Published in: WALCOM: Algorithms and Computation
Publisher: Springer Berlin Heidelberg
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A tree is a connected acyclic graph. A tree of
n
vertices is said to be graceful if the vertices can be assigned the labels { 0, 1, 2, ...,
n
− 1} such that the absolute value of the differences in vertex labels between neighboring vertices generate the set consisting distinct values { 1, 2, 3, ...,
n
− 1}. Ringel-Kotzig conjectured that all trees are graceful. In this paper we give a partial solution of the conjecture by proving that two large subclasses of trees are graceful.