Titlebook: Graceful, Harmonious and Magic TypeLabelings; Relations and Techni Susana C. López,Francesc A. Muntaner-Batle Book 2017 The Author(s) 2017

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Harmonious Labelings,te only a short chapter to this important labeling. We start answering the question of which complete graphs are harmonious. Later we will study a few families of harmonious graphs as well as general properties of these graphs. We will conclude this chapter providing an asymptotic answer to the question of how many graphs are harmonious.

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Book 2017derstand properties of graph labelings. The classical results integrated with new techniques, complete proofs, numerous exercises, and a variety of open problems, will provide readers with a solid understanding of graph labelings..

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2191-8198 belings.Aimed toward upper undergraduate and graduate students in mathematics, this book examines the foremost forms of graph labelings including magic, harmonious, and graceful labelings.  An overview of basic graph theory concepts and notation is provided along with the origins of graph labeling.

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https://doi.org/10.1007/978-1-4684-4853-5Graceful labelings of graphs appeared in 1967 due to the relationship found with the problem of decompositions of graphs, in particular with the problem of decomposing complete graphs into copies of a given tree. Strong relations between graceful labelings and Golomb rulers (which are a different way to understand Sidon sets) were also found.

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Carsten Carlberg,Ferdinand MolnárSince the beginning of graph labelings, researchers interested in this topic have dedicated their efforts mainly on finding techniques to prove the existence of particular families of graphs admitting some specific types of labeling. However, very few general techniques are known in order to create labelings of graphs.

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Carsten Carlberg,Ferdinand MolnárIn Chap. . we discussed the existence of labelings by utilizing the ⊗.-product of digraphs, which could be expressed algebraically as a generalization of voltage assignments, a classical technique used in topological graph theory. In this chapter, we introduce an algebraic method: Combinatorial Nullstellensatz.