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On consecutive edge magic total labeling of connected bipartite graphs

2014/10/03 by Bumtle Kang, Kang, Bumtle, Suh-Ryung Kim +3
Mathematics · #05C78 #Combinatorics (math.CO) #FOS: Mathematics #G.2.2 #acm:05C78 #math.CO #msc:05C78

paper · pdf · doi:10.48550/arxiv.1410.0766

14 pages, 2 figures

arxiv created 2014/10/03 · arxiv updated 2014/10/06

Abstract

Since Sedlá\brevecek 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 very 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, especially caterpillars and lobsters, which extends the results given by Sugeng and Miller.

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