A characterization of complete tripartite degree-magic graphs

Ľudmila Bezegová; Jaroslav Ivančo

Discussiones Mathematicae Graph Theory (2012)

  • Volume: 32, Issue: 2, page 243-253
  • ISSN: 2083-5892

Abstract

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A graph is called degree-magic if it admits a labelling of the edges by integers 1, 2,..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal to (1+ |E(G)|)/2*deg(v). Degree-magic graphs extend supermagic regular graphs. In this paper we characterize complete tripartite degree-magic graphs.

How to cite

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Ľudmila Bezegová, and Jaroslav Ivančo. "A characterization of complete tripartite degree-magic graphs." Discussiones Mathematicae Graph Theory 32.2 (2012): 243-253. <http://eudml.org/doc/270784>.

@article{ĽudmilaBezegová2012,
abstract = {A graph is called degree-magic if it admits a labelling of the edges by integers 1, 2,..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal to (1+ |E(G)|)/2*deg(v). Degree-magic graphs extend supermagic regular graphs. In this paper we characterize complete tripartite degree-magic graphs.},
author = {Ľudmila Bezegová, Jaroslav Ivančo},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {supermagic graphs; degree-magic graphs; complete tripartite graphs},
language = {eng},
number = {2},
pages = {243-253},
title = {A characterization of complete tripartite degree-magic graphs},
url = {http://eudml.org/doc/270784},
volume = {32},
year = {2012},
}

TY - JOUR
AU - Ľudmila Bezegová
AU - Jaroslav Ivančo
TI - A characterization of complete tripartite degree-magic graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2012
VL - 32
IS - 2
SP - 243
EP - 253
AB - A graph is called degree-magic if it admits a labelling of the edges by integers 1, 2,..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal to (1+ |E(G)|)/2*deg(v). Degree-magic graphs extend supermagic regular graphs. In this paper we characterize complete tripartite degree-magic graphs.
LA - eng
KW - supermagic graphs; degree-magic graphs; complete tripartite graphs
UR - http://eudml.org/doc/270784
ER -

References

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  1. [1] Ľ. Bezegová and J. Ivančo, An extension of regular supermagic graphs, Discrete Math. 310 (2010) 3571-3578, doi: 10.1016/j.disc.2010.09.005. Zbl1200.05199
  2. [2] Ľ. Bezegová and J. Ivančo, On conservative and supermagic graphs, Discrete Math. 311 (2011) 2428-2436, doi: 10.1016/j.disc.2011.07.014. Zbl1238.05226
  3. [3] T. Bier and A. Kleinschmidt, Centrally symmetric and magic rectangles, Discrete Math. 176 (1997) 29-42, doi: 10.1016/S0012-365X(96)00284-1. Zbl0898.05007
  4. [4] J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. 17 (2010) #DS6. Zbl0953.05067
  5. [5] T.R. Hagedorn, Magic rectangles revisited, Discrete Math. 207 (1999) 65-72, doi: 10.1016/S0012-365X(99)00041-2. Zbl0942.05009
  6. [6] J. Ivančo, On supermagic regular graphs, Math. Bohemica 125 (2000) 99-114. Zbl0963.05121
  7. [7] J. Sedláček, Problem 27. Theory of graphs and its applications, Proc. Symp. Smolenice, Praha (1963) 163-164. 
  8. [8] B.M. Stewart, Magic graphs, Canad. J. Math. 18 (1966) 1031-1059, doi: 10.4153/CJM-1966-104-7. Zbl0149.21401
  9. [9] 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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