Supermagic graphs with many odd degrees

Dalibor Froncek; Jiangyi Qiu

doi:10.1007/978-3-030-25005-8_19

Supermagic graphs with many odd degrees

Dalibor Froncek, Jiangyi Qiu

Mathematics & Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

3 Scopus citations

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)
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	https://doi.org/10.1007/978-3-030-25005-8_19
State	Published - 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)
Volume	11638 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	30th International Workshop on Combinatorial Algorithms, IWOCA 2019
Country/Territory	Italy
City	Pisa
Period	7/23/19 → 7/25/19

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

Keywords

Edge labeling
Magic-type labeling
Supermagic graphs

Publisher link

10.1007/978-3-030-25005-8_19

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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

Supermagic graphs with many odd degrees. / Froncek, Dalibor; Qiu, Jiangyi.
Combinatorial Algorithms - 30th International Workshop, IWOCA 2019, Proceedings. ed. / Charles J. Colbourn; Roberto Grossi; Nadia Pisanti. Springer Verlag, 2019. p. 229-236 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11638 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Froncek, D & Qiu, J 2019, Supermagic graphs with many odd degrees. in CJ Colbourn, R Grossi & N Pisanti (eds), Combinatorial Algorithms - 30th International Workshop, IWOCA 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11638 LNCS, Springer Verlag, pp. 229-236, 30th International Workshop on Combinatorial Algorithms, IWOCA 2019, Pisa, Italy, 7/23/19. https://doi.org/10.1007/978-3-030-25005-8_19

Froncek D, Qiu J. Supermagic graphs with many odd degrees. In Colbourn CJ, Grossi R, Pisanti N, editors, Combinatorial Algorithms - 30th International Workshop, IWOCA 2019, Proceedings. Springer Verlag. 2019. p. 229-236. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-25005-8_19

Froncek, Dalibor ; Qiu, Jiangyi. / Supermagic graphs with many odd degrees. Combinatorial Algorithms - 30th International Workshop, IWOCA 2019, Proceedings. editor / Charles J. Colbourn ; Roberto Grossi ; Nadia Pisanti. Springer Verlag, 2019. pp. 229-236 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Supermagic graphs with many odd degrees",

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, Kov{\'a}{\v r} 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.",

keywords = "Edge labeling, Magic-type labeling, Supermagic graphs",

author = "Dalibor Froncek and Jiangyi Qiu",

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AB - 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.

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Supermagic graphs with many odd degrees

Abstract

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