### Abstract

A graph G = (V,E) is called supermagic if there exists a bijection f : E → {1, 2, … , |E|} such that the weight of every vertex x ∈ V defined as the sum of labels f(xy) of all edges xy incident with x is equal to the same number m, called the supermagic constant. Recently, Kovář et al. affirmatively answered a question by Madaras about existence of supermagic graphs with arbitrarily many different degrees. Their construction provided graphs with all degrees even. Therefore, they asked if there exists a supermagic graph with d different odd degrees for any positive integer d. We answer this question in the affirmative by providing a construction based on the use of 3-dimensional magic rectangles.

Original language | English (US) |
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Title of host publication | Combinatorial Algorithms - 30th International Workshop, IWOCA 2019, Proceedings |

Editors | Charles J. Colbourn, Roberto Grossi, Nadia Pisanti |

Publisher | Springer- Verlag |

Pages | 229-236 |

Number of pages | 8 |

ISBN (Print) | 9783030250041 |

DOIs | |

State | Published - Jan 1 2019 |

Event | 30th International Workshop on Combinatorial Algorithms, IWOCA 2019 - Pisa, Italy Duration: Jul 23 2019 → Jul 25 2019 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11638 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 30th International Workshop on Combinatorial Algorithms, IWOCA 2019 |
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Country | Italy |

City | Pisa |

Period | 7/23/19 → 7/25/19 |

### Keywords

- Edge labeling
- Magic-type labeling
- Supermagic graphs

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## Cite this

*Combinatorial Algorithms - 30th International Workshop, IWOCA 2019, Proceedings*(pp. 229-236). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11638 LNCS). Springer- Verlag. https://doi.org/10.1007/978-3-030-25005-8_19