Supermagic graphs with many odd degrees

Dalibor Froncek, Jiangyi Qiu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publicationCombinatorial Algorithms - 30th International Workshop, IWOCA 2019, Proceedings
EditorsCharles J. Colbourn, Roberto Grossi, Nadia Pisanti
PublisherSpringer- Verlag
Pages229-236
Number of pages8
ISBN (Print)9783030250041
DOIs
StatePublished - Jan 1 2019
Event30th International Workshop on Combinatorial Algorithms, IWOCA 2019 - Pisa, Italy
Duration: Jul 23 2019Jul 25 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11638 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference30th International Workshop on Combinatorial Algorithms, IWOCA 2019
CountryItaly
CityPisa
Period7/23/197/25/19

Keywords

  • Edge labeling
  • Magic-type labeling
  • Supermagic graphs

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  • Cite this

    Froncek, D., & Qiu, J. (2019). Supermagic graphs with many odd degrees. In C. J. Colbourn, R. Grossi, & N. Pisanti (Eds.), 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