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Magic and supermagic dense bipartite graphs

Jaroslav Ivanco

Discussiones Mathematicae Graph Theory (2007)

  • Volume: 27, Issue: 3, page 583-591
  • ISSN: 2083-5892

Abstract

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A graph is called magic (supermagic) if it admits a labelling of the edges by pairwise different (and consecutive) positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In the paper we prove that any balanced bipartite graph with minimum degree greater than |V(G)|/4 ≥ 2 is magic. A similar result is presented for supermagic regular bipartite graphs.

How to cite

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Jaroslav Ivanco. "Magic and supermagic dense bipartite graphs." Discussiones Mathematicae Graph Theory 27.3 (2007): 583-591. <http://eudml.org/doc/270151>.

@article{JaroslavIvanco2007,
abstract = {A graph is called magic (supermagic) if it admits a labelling of the edges by pairwise different (and consecutive) positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In the paper we prove that any balanced bipartite graph with minimum degree greater than |V(G)|/4 ≥ 2 is magic. A similar result is presented for supermagic regular bipartite graphs.},
author = {Jaroslav Ivanco},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {magic graphs; supermagic graphs; bipartite graphs},
language = {eng},
number = {3},
pages = {583-591},
title = {Magic and supermagic dense bipartite graphs},
url = {http://eudml.org/doc/270151},
volume = {27},
year = {2007},
}

TY - JOUR
AU - Jaroslav Ivanco
TI - Magic and supermagic dense bipartite graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2007
VL - 27
IS - 3
SP - 583
EP - 591
AB - A graph is called magic (supermagic) if it admits a labelling of the edges by pairwise different (and consecutive) positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In the paper we prove that any balanced bipartite graph with minimum degree greater than |V(G)|/4 ≥ 2 is magic. A similar result is presented for supermagic regular bipartite graphs.
LA - eng
KW - magic graphs; supermagic graphs; bipartite graphs
UR - http://eudml.org/doc/270151
ER -

References

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  1. [1] A. Czygrinow and H.A. Kierstead, 2-factors in dense bipartite graphs, Discrete Math. 257 (2002) 357-369, doi: 10.1016/S0012-365X(02)00435-1. Zbl1008.05119
  2. [2] M. Doob, Characterizations of regular magic graphs, J. Combin. Theory (B) 25 (1978) 94-104, doi: 10.1016/S0095-8956(78)80013-6. Zbl0384.05054
  3. [3] J.A. Gallian, A dynamic survey of graph labeling, Electronic J. Combinatorics #DS6 36 (2003). Zbl0953.05067
  4. [4] N. Hartsfield and G. Ringel, Pearls in Graph Theory (Academic Press, Inc., San Diego, 1990). Zbl0703.05001
  5. [5] J. Ivanco, On supermagic regular graphs, Mathematica Bohemica 125 (2000) 99-114. Zbl0963.05121
  6. [6] J. Ivanco, Z. Lastivková and A. Semanicová, On magic and supermagic line graphs, Mathematica Bohemica 129 (2004) 33-42. 
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  8. [8] S. Jezný and M. Trenkler, Characterization of magic graphs, Czechoslovak Math. J. 33 (1983) 435-438. Zbl0571.05030
  9. [9] J. Moon and L. Moser, On Hamiltonian bipartite graphs, Isr. J. Math. 1 (1963) 163-165, doi: 10.1007/BF02759704. Zbl0119.38806
  10. [10] J. Sedlácek, On magic graphs, Math. Slovaca 26 (1976) 329-335. Zbl0348.05114
  11. [11] J. Sedlácek, Problem 27, in: Theory of Graphs and Its Applications, Proc. Symp. Smolenice (Praha, 1963) 163-164. 
  12. [12] B.M. Stewart, Magic graphs, Canad. J. Math. 18 (1966) 1031-1059, doi: 10.4153/CJM-1966-104-7. Zbl0149.21401
  13. [13] B.M. Stewart, Supermagic complete graphs, Canad. J. Math. 19 (1967) 427-438, doi: 10.4153/CJM-1967-035-9. Zbl0162.27801

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