Discussiones Mathematicae Graph Theory 32(2) (2012) 243-253
doi: 10.7151/dmgt.1608

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A Characterization of Complete Tripartite Degree-magic Graphs

L'udmila Bezegová and Jaroslav Ivančo

Institute of Mathematics,
P. J. Šafárik University, Jesenná 5,
040 01 Košice, Slovakia


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 deg(v)(1+ |E(G)|)/2. Degree-magic graphs extend supermagic regular graphs. In this paper we characterize complete tripartite degree-magic graphs.

Keywords: supermagic graphs, degree-magic graphs, complete tripartite graphs

2010 Mathematics Subject Classification: 05C78.


[1]L'. Bezegová and J. Ivančo, An extension of regular supermagic graphs, Discrete Math. 310 (2010) 3571--3578, doi: 10.1016/j.disc.2010.09.005.
[2]L'. Bezegová and J. Ivančo, On conservative and supermagic graphs, Discrete Math. 311 (2011) 2428--2436, doi: 10.1016/j.disc.2011.07.014.
[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.
[4]J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. 17 (2010) #DS6.
[5]T.R. Hagedorn, Magic rectangles revisited, Discrete Math. 207 (1999) 65--72, doi: 10.1016/S0012-365X(99)00041-2.
[6]J. Ivančo, On supermagic regular graphs, Math. Bohemica 125 (2000) 99--114.
[7]J. Sedláček, Problem 27. Theory of graphs and its applications, Proc. Symp. Smolenice, Praha (1963) 163--164.
[8]B.M. Stewart, Magic graphs, Canad. J. Math. 18 (1966) 1031--1059, doi: 10.4153/CJM-1966-104-7.
[9]B.M. Stewart, Supermagic complete graphs, Canad. J. Math. 19 (1967) 427--438, doi: 10.4153/CJM-1967-035-9.

Received 14 December 2010
Revised 7 April 2011
Accepted 28 April 2011