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Discussiones Mathematicae Graph Theory 27(3) (2007) 583-591
DOI: https://doi.org/10.7151/dmgt.1384

MAGIC AND SUPERMAGIC DENSE BIPARTITE GRAPHS

Jaroslav Ivanco

Institute of Mathematics
P.J. Safárik University, Jesenná 5
SK-041 54 Košice, Slovak Republic
e-mail: jaroslav.ivanco@upjs.sk

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.

Keywords: magic graphs, supermagic graphs, bipartite graphs.

2000 Mathematics Subject Classification: 05C78.

References

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Received 31 January 2006
Revised 30 November 2006
Accepted 17 January 2007