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

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 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.

References

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