On consecutive edge magic total labelings of connected bipartite graphs

Since Sedlá\(\breve{\hbox {c}}\)ek introduced the notion of magic labeling of a graph in 1963, a variety of magic labelings of a graph have been defined and studied. In this paper, we study consecutive edge magic labelings of a connected bipartite graph. We make a useful observation that there are only four possible values of b for which a connected bipartite graph has a b-edge consecutive magic labeling. On the basis of this fundamental result, we deduce various interesting results on consecutive edge magic labelings of bipartite graphs. As a matter of fact, we do not focus just on specific classes of graphs, but also discuss the more general classes of non-bipartite and bipartite graphs.

This work was partially supported by the National Research Foundation of Korea(NRF) Grant funded by the Korea government (MEST) (No. NRF-2010-0009933).

Authors and Affiliations

1. Department of Mathematics Education, Seoul National University, Seoul, 151-742, Korea

   Bumtle Kang & Suh-Ryung Kim

2. Department of Mathematics, Kyung Hee University, Seoul, 130-701, Korea

   Ji Yeon Park

Corresponding author

Correspondence to Ji Yeon Park.

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