Abstract
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.
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Aryabhatta, S., Guha Roy, T., Uddin, M.M., Rahman, M.S. (2011). On Graceful Labelings of Trees. In: Katoh, N., Kumar, A. (eds) WALCOM: Algorithms and Computation. WALCOM 2011. Lecture Notes in Computer Science, vol 6552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19094-0_22
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DOI: https://doi.org/10.1007/978-3-642-19094-0_22
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