## Graceful, Harmonious and Magic Type Labelings: Relations and TechniquesAimed 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. Common methods and techniques are presented introducing readers to links between graph labels. A variety of useful techniques are presented to analyze and understand 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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### Contents

1 | |

2 Graphs Labelings | 14 |

First Type of Relations | 33 |

4 Harmonious Labelings | 53 |

The Shifting Technique | 64 |

Second Type of Relations | 91 |

7 The Polynomial Method | 123 |

### Other editions - View all

Graceful, Harmonious and Magic Type Labelings: Relations and Techniques Susana C. López,Francesc A. Muntaner-Batle No preview available - 2017 |

Graceful, Harmonious and Magic Type Labelings: Relations and Techniques Susana C. Lopez,Francesc A. Muntaner-Batle No preview available - 2017 |

### Common terms and phrases

0-valuation 2-regular graphs adjacency matrix appears in Fig assigned Assume Baˇca bijective function Cartesian product caterpillar Comb Combinatorial Nullstellensatz complete bipartite graphs complete graphs consider Corollary cycle Cn defined Definition degree sequence denoted digraph Discrete Math elements Example Exercise exists f W V.G families of graphs Figueroa-Centeno following result function h graceful graphs graceful labeling graph G graph obtained graph theory h-product harmonious graphs harmonious labeling Hence Ichishima induced edge labels integer isomorphic k-equitable Kotzig labeling f labeling of G Lemma Let f Let G López magic labelings magic sum Muntaner-Batle nonisomorphic open problems p;q/-graph G pair partition path path-like tree permutation Petersen graph polynomial Proof Let prove S)(S)EM labelings sequential labeling shows Sidon set special super edge-magic stable sets subgraph super edge super edge-magic graphs super edge-magic labeling techniques Theorem Tp-trees vertex labels vertex set vertex-magic total labeling vertices weak Sidon set