On consecutive edge magic total labelings of connected bipartite graphs

Bumtle Kang (), Suh-Ryung Kim () and Ji Yeon Park ()
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Bumtle Kang: Seoul National University
Suh-Ryung Kim: Seoul National University
Ji Yeon Park: Kyung Hee University

Journal of Combinatorial Optimization, 2017, vol. 33, issue 1, No 2, 13-27

Abstract: Abstract Since Sedlá $$\breve{\hbox {c}}$$ 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.

Keywords: Consecutive edge magic total labeling; Super edge-magic labeling; Magic constant; Graceful labeling; Bipartite graphs; Caterpillar; Double star; Lobster; 05C78 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-015-9928-0

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